The Pope in Rome has (arguably) succession all the way back to Peter. I am wondering what the earliest acknowledgment of some kind of pastoral power over the church in Rome, whether it be in letter or in some other form of writing. There doesn't necessarily need to be a claim of "Pope", but rather an acknowledgement of such authority or a title of office.
What is the earliest example of the observance of a Pope in Rome?
First of all, a little history on the team pope.
Pope is a title traditionally accorded to the Bishop of Rome, the Coptic and Greek Orthodox Bishop of Alexandria, and some autocratic leaders of other ecclesial communities. Popes may also claim the title Patriarch. Both terms come from a word for father.
The word pope is derived ultimately from the Greek πάππας (páppas) originally an affectionate term meaning "father", later referring to a bishop or patriarch. The earliest record of the use of this title is in regard to the Patriarch of Alexandria, Pope Heraclas of Alexandria (232–248) in a letter written by his successor, Pope Dionysius of Alexandria, to Philemon, a Roman presbyter:
τοῦτον ἐγὼ τὸν κανόνα καὶ τὸν τύπον παρὰ τοῦ μακαρίου πάπα ἡμῶν Ἡρακλᾶ παρέλαβον.
Which translates into:
I received this rule and ordinance from our blessed father/pope, Heraclas.
From the early 3rd century the title was applied generically to all bishops. The earliest extant record of the word papa being used in reference to a Bishop of Rome dates to late 3rd century, when it was applied to Pope Marcellinus.
According to the Oxford English Dictionary, the earliest recorded use of the title "pope" in English is in an Old English translation (c. 950) of Bede's Ecclesiastical History of the English People:
Þa wæs in þa tid Uitalius papa þæs apostolican seðles aldorbiscop.
Later history and contemporary use Edit
The title pope continues to be used by Alexandrian bishops; both the Coptic Orthodox and Greek Orthodox Patriarchs of Alexandria are known as the "Pope and Patriarch of Alexandria".
In the Western Christian world "pope" is chiefly associated with the Bishops of Rome — from the 5th or 6th century it became, in the West, a title reserved exclusively for these bishops. Despite its earlier use to refer to any bishop, in 998 an Archbishop of Milan was rebuked for having called himself "pope", and in 1073 it was formally decided by Pope Gregory VII that no other bishop of the Catholic Church would hold the title.
In the Slavic languages of many Eastern Orthodox countries the term "pope" (поп, піп; pop) means "priest"; these include Russian, Ukrainian, Serbian, and Bulgarian. The Romanian popă has the same meaning. When context is clear, "pope" may also be used in English to mean "Eastern Orthodox priest".
There is as of today still a Pope of the Coptic Orthodox Church!
Now for the aspect of the Bishop of Rome as having preeminence amongst other Catholic Bishops.
The doctrines of Petrine primacy and papal primacy are perhaps the most contentiously disputed in the history of Christianity. Theologians regard the doctrine of papal primacy as having gradually developed in the West due to the convergence of a number of factors, e.g., the dignity of Rome as the only apostolic see in the West; the tradition that both Peter and Paul had been martyred there; Rome's long history as a capital of the Roman Empire; and its continuing position as the chief center of commerce and communication.
Primacy of Peter the apostle
According to numerous records of the early Church Fathers, Peter was present in Rome, was martyred there, and was the first bishop of Rome. Dogma and traditions of the Catholic Church maintain that he served as the bishop of Rome for 25 years until 67 AD when he was martyred by Nero (further information: Great Fire of Rome). The official Catholic position, as Eamon Duffy points out in his book Saints and Sinners: A History of the Popes, is that Jesus had essentially appointed Peter as the first pope, though the respectful title "pope" (meaning, "father") developed at a later time. The New Testament evidence is briefly summarized:
Roman Catholic doctrine maintains that the universal primacy of the bishop of Rome was divinely instituted by Jesus Christ. This was derived from the Petrine texts, and from the gospel accounts of Matthew (16:17‑19), Luke (22:32)and John (21:15‑17) according to the Roman tradition, they all refer not simply to the historical Peter, but to his successors to the end of time. Today, scriptural scholars of all traditions agree that we can discern in the New Testament an early tradition which attributes a special position to Peter among Christ's twelve apostles. The Church built its identity on them as witnesses, and responsibility for pastoral leadership was not restricted to Peter. In Matthew 16:19, Peter is explicitly commissioned to "bind and loose"; later, in Matthew 18:18, Christ directly promises all the disciples that they will do the same. Similarly, the foundation upon which the Church is built is related to Peter in Matthew 16:16, and to the whole apostolic body elsewhere in the New Testament (cf. Eph. 2:10). — Rev. Emmanuel Clapsis
The New Testament does not contain an explicit record of the transmission of Peter's leadership, nor is the transmission of apostolic authority in general very clear. As a result, the Petrine texts of the New Testament have been subjected to differing interpretations from the time of the Church Fathers on.
At least by the late second century, belief that Jesus granted Peter jurisdiction over the Church is reflected, when Clement of Alexandria wrote: "Who is the Rich man that is Saved? The blessed Peter, the chosen, the pre-eminent, the first of the disciples, for whom alone and Himself the Saviour paid tribute, [who] quickly seized and comprehended the saying" (Ch. 21), referring to Mk 10:28. Tertullian, while examining Scriptural teachings, legal precedents, and dogma surrounding monogamy and marriage (post AD 213), says of Peter, "Monogamist I am led to presume him by consideration of the Church, which, built upon him..." ("On Monogamy", Ch. 8): his certainty that the Church is built especially upon Peter is such that he simply refers to it in the context of another discussion. In a slightly later text (AD 220) "On Modesty", Tertullian writes at length about the significance of Matthew 16:18-19, "On this rock I will build my Church", and similar, emphasizing the singular, not plural, right, and condemning "wholly changing the manifest intention of the Lord, conferring (as that intention did) this (gift) personally upon Peter" (Ch. 21). Origen (c. AD 232) wrote also of "Peter, upon whom is built the Church of Christ" (Jurgens §479a).
Irenaeus compiled a list of succession of the bishops of Rome, including the immediate successors of Peter and Paul: Linus, Anacleutus, Clement, Evaristus, Alexander, and Sixtus.3 The Catholic Church currently considers these the successors of Peter, whom they consider the first pope, and through whom following popes would claim authority.
The evolution of earlier tradition established both Peter and Paul as the forefathers of the bishops of Rome, from whom they received their position as chief shepherd (Peter) and supreme authority on doctrine (Paul). To establish her primacy among the churches of the Western half of the empire, the bishops of Rome relied on a letter written in 416 by Innocent I to the Bishop of Gubbio, to show how subordination to Rome had been established. Since Peter was the only apostle (no mention of Paul) to have worked in the West, thus the only persons to have established churches in Italy, Spain, Gaul, Sicily, Africa, and the Western islands were bishops appointed by Peter or his successors. This being the case then, all congregations had to abide by the regulations set in Rome).
Rome's role as arbiter
This passage in Irenaeus (from Against Heresies 3:4:1) illuminates the meaning of his remarks about the Church of Rome: if there are disputes in a local church, that church should have recourse to the Roman Church, for there is contained the Tradition which is preserved by all the churches. Rome's vocation [in the pre-Nicene period] consisted in playing the part of arbiter, settling contentious issues by witnessing to the truth or falsity of whatever doctrine was put before them. Rome was truly the center where all converged if they wanted their doctrine to be accepted by the conscience of the Church. They could not count upon success except on one condition, that the Church of Rome had received their doctrine. And refusal from Rome predetermined the attitude the other churches would adopt. There are numerous cases of this recourse to Rome... — Fr. Nicholas Afanassieff, The Primacy of Peter (c. 1992)
In the aftermath of the Decian persecution there were disagreements regarding how to deal with those who had lapsed; whether and under what conditions might they be readmitted to the Christian community. At the behest of Faustinus of Lyon and other bishops of Gaul, Cyprian of Carthage wrote Pope Stephen I (254-257) asking him to instruct the bishops of Gaul to condemn Marcianus of Arles (who refused to admit those who repented) and to elect another bishop in his stead. In 250, St. Cyprian and St. Firmilian both wrote of the Bishop of Rome as successor of Peter, and the latter mentions how the Bishop of Rome decreed policy for other regions based on this succession.
In 376, Jerome was living as an ascetic in the desert of Chalcis, south-west of Antioch. Pope Damasus I had asked him to make a new translation of scripture. At that there were rival claimants for the See of Antioch, and Jerome wrote Pope Damasus I to ask who was the true bishop of the three claimants of the see of Antioch, and for clarification of a doctrinal issue:
Yet, though your greatness terrifies me, your kindness attracts me. From the priest I demand the safe-keeping of the victim, from the shepherd the protection due to the sheep. ...My words are spoken to the successor of the fisherman, to the disciple of the cross. As I follow no leader save Christ, so I communicate with none but your blessedness, that is with the chair of Peter. For this, I know, is the rock on which the church is built! This is the house where alone the paschal lamb can be rightly eaten. This is the ark of Noah, and he who is not found in it shall perish when the flood prevails. But since by reason of my sins I have betaken myself to this desert which lies between Syria and the uncivilized waste, I cannot, owing to the great distance between us, always ask of your sanctity the holy thing of the Lord. ...He that gathers not with you scatters; he that is not of Christ is of Antichrist.
In 382 Jerome accompanied one of the claimants, Paulinus II of Antioch, to Rome, where Pope Damasus I (366-384) had convened a council to determine a canonical list of scripture. (Jerome then served as confidential secretary to the Pope for the next three years before heading to Bethlehem.)
Saint Optatus clearly believed in a "Chair of Peter", calling it a gift of the Church and saying, as summarized by Henry Wace, that "Parmenian must be aware that the episcopal chair was conferred from the beginning on Peter, the chief of the apostles, that unity might be preserved among the rest and no one apostle set up a rival." "You cannot deny that you are aware that in the city of Rome the episcopal chair was given first to Peter, the chair in which Peter sat, the same who was head—that is why he is also called Cephas—of all the Apostles; the one chair in which unity is maintained by all. Neither do other Apostles proceed individually on their own; and anyone who would set up another chair in opposition to that single chair would, by that very fact, be a schismatic and a sinner."
To be fair this Wikipedia article should be a little more clear. St. Irenæus does not say explicitly the Church of Rome in his Against Heresies (Book III, Chapter 4). Being the Bishop of Lugdunum, Gaul (Lyon, France), it is understood by Church historians to imply The Church of Rome. He employs the phrase ”ancient Churches with which the apostles held constant intercourse”; thus Rome is clearly the closest Apostolic see founded by an Apostle to the City of Lyon.
Suppose there arise a dispute relative to some important question among us, should we not have recourse to the most ancient Churches with which the apostles held constant intercourse, and learn from them what is certain and clear in regard to the present question? For how should it be if the apostles themselves had not left us writings? Would it not be necessary, [in that case,] to follow the course of the tradition which they handed down to those to whom they did commit the Churches? - Against Heresies (Book I, Chapter 3)
Pope Siricius declared that no bishop could take office without his knowledge. (Still looking for a primary on-line source.)
Siricius was a Roman, the son of Tiburtius. He entered the service of the Church as a youth and served as a deacon from the time of Pope Liberius. He was unanimously elected to succeed Pope Damasus in December of 384.
St. Siricius is noted for being the author of the first papal decretal which has survived. There were earlier ones, but this is the first that has come down to modern times. A decretal contains an authoritative decision on questions of discipline. The occasion of this decretal was a letter from Himerius, bishop of Tarragona in Spain, who wrote to Pope Damasus asking for his decision in several matters of discipline. Siricius answered on February 10, and ordered that his reply should be communicated to the neighboring bishops. Among other things the Pope declared that converted Arians did not have to be rebaptized and that priests should be celibate.
On January 6, 386, Pope Siricius held a synod at Rome, attended by eighty bishops, at which a number of disciplinary decisions were made. The Pope sent these decisions to the bishops of North Africa. He also sent out a letter to various churches urging the election of worthy bishops and priests. But around 388, Siricius was to have something to worry about at home. A monk named Jovinian, who had enjoyed a reputation for a strict life, came to Rome and began to teach that after all a strict life was useless. Vows, virginity, fasting, and good works were of small avail. Jovinian, quite consistently, gave up his strict life and not content with taking it easy himself began to persuade a number of monks and nuns to give it all up and get married. Lay people, scandalized at this, urged Siricius to do something. The Pope then held a synod in 390 which condemned the theories of Jovinian and excommunicated him and his chief followers. Siricius then sent three priests to Milan to tell St. Ambrose about the synod. Ambrose himself held a synod which praised the Pope for his watchfulness and repeated the condemnation of Jovian.
The Catholic Encyclopedia has an excellent lengthy article on the subject of the pope:
In the middle of the third century St. Cyprian expressly terms the Roman See the Chair of St. Peter, saying that Cornelius has succeeded to "the place of Fabian which is the place of Peter" (Epistle 51:8; cf. 75:3).
St. Robert Cardinal Bellarmine cites "the testimonies of the ancient Roman Bishops who were martyrs or confessors" of St. Peter's ruling from Rome, in De Romano Pontifice bk. 2 ch. 4:
Pope Clement teaches that with death threatening he [St. Peter] handed on the Roman Episcopate to him.556 Anacletus in Epistle 3 teaches that on account of the see of Peter, the Roman Church is the head of all others. Marcellus I, in a letter to the Antiochenes, says: “The See of Peter was begun with you, and was transferred to Rome at the Lord’s command, etc.” Pope Damasus says that Peter was the Bishop of Rome for twenty-five years, that is, even to his death.557 Innocent I, teaches the same thing, in a letter to the Council of Miletus.558 Moreover, so do Pope Leo, Gelasius, John III, Pope St Gregory, Agatho, Adrian and Nicholas I, and all others who wrote anything, affirm that their See is the Seat of Peter.559
556. Constit. Apostolic., bk 7, ch. 46.
557. In pontificali in Petro.
558. This is 93 among the epistles of Augustine.
559. Leo, serm. 1 de natali Apostolorum; Gelasius Epistola ad Episcopos Germaniae et Galliae; Gregory bk 2, epist. 33; Agatho in epistola ad Constantinum imperatorem; Adrian epistola ad Tharasium; Nicholas I, Epistola ad Michaelem.
See also Saint Peter and the First Years of Christianity by Constant Fouard.