What was the early Church Fathers' understanding of the “baptism with Holy Spirit and fire”?
The terms ”baptism by fire” and ”baptism of fire” are derived from the Bible, from the New Testament book of Matthew 3:11.
Baptism by fire and baptism of fire are two idioms that mean the same thing. Baptism by fire is more often used in the United States and baptism of fire is more often used in Britain. An idiom is a word, group of words or phrase that has a figurative meaning that is not easily deduced from its literal meaning. We will examine the meaning of baptism by fire and baptism of fire, where these terms came from and some examples of their use in sentences.
Baptism by fire and baptism of fire describe something being experienced for the first time that is very difficult. Most often, enduring a baptism by fire means to be thrown into a situation with little or no preparation and surviving it through one’s wits and gumption. Previously, baptism by fire referred to experiencing battle for the first time or to endure martyrdom. The terms baptism by fire and baptism of fire are derived from the Bible, from the New Testament book of Matthew 3:11: “I indeed baptize you with water unto repentance: but he that cometh after me is mightier than I, whose shoes I am not worthy to bear: he shall baptize you with the Holy Ghost, and with fire.” The fire in this passage refers to the fire or inspiration of the Holy Spirit. - Baptism by fire and baptism of fire
There seem to be no “Early Church Fathers” (with your time frame intended) that deal with with this subject matter. The extremely Early Church Fathers do not seem to employ the expression(s) as is mentioned in this subject matter. Nevertheless, the phrase Does occur several times in Scriptures.
As for what the other Church Fathers thought of these terms the following may be of assistance:
Commentary from the Church Fathers
Glossa Ordinaria: As in the preceding words John had explained more at length what he had shortly preached in the words, Repent ye, so now follows a more full enlargement of the words, The kingdom of heaven is at hand.
Gregory the Great: John baptizes not with the Spirit but with water, because he had no power to forgive sins; he washes the body with water, but not at the same time the soul with pardon of sin.
Chrysostom: For while as yet the sacrifice had not been offered, nor remission of sin sent, nor the Spirit had descended on the water, how could sin be forgiven? But since the Jews never perceived their own sin, and this was the cause of all their evils, John came to bring them to a sense of them by calling them to repentance.
Gregory the Great: Why then does he baptize who could not remit sin, but that he may preserve in all things the office of forerunner? As his birth had preceded Christ's birth, so his baptism should precede the Lord's baptism.
Pseudo-Chrysostom: Or, John was sent to baptize, that to such as came to his baptism he might announce the presence among them of the Lord in the flesh, as himself testifies in another place, That He might be manifested to Israel, therefore am I come to baptise with water. (John 1:31.)
Augustine: Or, he baptizes, because it behoved Christ to be baptized. But if indeed John was sent only to baptize Christ, why was not He alone baptized by John? Because had the Lord alone been baptized by John, there would not have lacked who should insist that John's baptism was greater than Christ's, inasmuch as Christ alone had the merit to be baptized by it.
Rabanus Maurus: Or, by this sign of baptism he separates the penitent from the impenitent, and directs them to the baptism of Christ.
Pseudo-Chrysostom: Because then he baptized on account of Christ, therefore to them who came to him for baptism he preached that Christ should come, signifying the eminence of His power in the words, He who cometh after me is mightier than I.
Saint Remigius: There are five points in which Christ comes after John, His birth, preaching, baptism, death, and descent into hell. A beautiful expression is that, mightier than I, because he is mere man, the other is God and man.
Rabanus Maurus: As though he had said, I indeed am mighty to invite to repentance, He to forgive sins; I to preach the kingdom of heaven, He to bestow it; I to baptize with water, He with the Spirit.
Chrysostom: When you hear for He is mightier than I, do not suppose this to be said by way of comparison, for I am not worthy to be numbered among his servants, that I might undertake the lowest office.
Hilary of Poitiers: Leaving to the Apostles the glory of bearing about the Gospel, to whose beautiful feet was due the carrying the tidings of God's peace.
Pseudo-Chrysostom: Or, by the feet of Christ we may understand Christians, especially the Apostles, and other preachers, among whom was John Baptist; and the shoes are the infirmities with which he loads the preachers. These shoes all Christ's preachers wear; and John also wore them; but declares himself unworthy, that he might show the grace of Christ, and be greater than his deserts.
Jerome: In the other Gospels it is, whose shoe latchet I am not worthy to loose. Here his humility, there his ministry is intended; Christ is the Bridegroom, and John is not worthy to loose the Bridegroom's shoe, that his house be not called according to the Law of Moses and the example of Ruth, The house of him that hath his shoe loosed. (Deut. 25:10.)
Jerome: Either the Holy Ghost Himself is a fire, as we learn from the Acts, when there sat as it were fire on the tongues of the believers; and thus the word of the Lord was fulfilled who said, I am come to send fire on the earth, I will that it burn. (Luke 12:49.) Or, we are baptized now with the Spirit, hereafter with fire; as the Apostle speaks, Fire shall try every man's work, of what sort it ise. (1 Cor. 3:13.)
Chrysostom: He does not say, shall give you the Holy Ghost, but shall baptize you in the Holy Ghost, showing in metaphor the abundance of the grace. fThis further shows, that even under the faith there is need of the will alone for justification, not of labours and toilings; and even as easy a thing as it is to be baptized, even so easy a thing it is to be changed and made better. By fire he signifies the strength of grace which cannot be overcome, and that it may be understood that He makes His own people at once like to the great and old prophets, most of the prophetic visions were by fire.
Hilary of Poitiers: He marks the time of our salvation and judgment in the Lord; those who are baptized in the Holy Ghost it remains that they be consummated by the fire of judgment.
The above lines by the Church Fathers can be found in the following book: Catena aurea, commentary on the four Gospels; collected out of the works of the Fathers
Addendum:
The Church Fathers, Early Church Fathers, Christian Fathers, or Fathers of the Church were ancient and influential Christian theologians and writers who established the intellectual and doctrinal foundations of Christianity. The historical period in which they worked became known as the Patristic Era and spans approximately from the late 1st to mid 8th centuries, flourishing in particular during the 4th and 5th centuries, when Christianity was in the process of establishing itself as the state church of the Roman Empire.
In traditional dogmatic theology, authors considered Church Fathers are treated as authoritative, and a somewhat restrictive definition is used. The academic field of patristics, the study of the Church Fathers, has extended the scope of the term, and there is no definitive list.
Eras of the Church Fathers
The church fathers are generally divided into the Ante-Nicene Fathers, those who lived and wrote before the Council of Nicaea (325) and the Nicene and Post-Nicene Fathers, those who lived and wrote after 325. Also, the division of the fathers into Greek and Latin writers is also common. Some of the most prominent Greek Fathers are Justin Martyr, Athanasius of Alexandria, Basil of Caesarea, Gregory of Nazianzus, John Chrysostom, Cyril of Alexandria, and Maximus the Confessor. Among the Latin Fathers are Tertullian, Cyprian, Jerome, Ambrose of Milan, Augustine of Hippo, and Gregory the Great.