I recently watched a video from the youtube channel Ascension Presents and Fr. Mike Schmitz on whether or not Catholics worship the saints. He quoted St. Augustine who said that we give the saints honor, Mary higher honor, and God worship (or something similar). My question is where was quoted from and what were the other Church Fathers' and early Church views on the veneration or honoring of Saints?
The Catholic concept we're talking about is dulia:
a theological term signifying the honour paid to the saints, while latria means worship given to God alone, and hyperdulia the veneration offered to the Blessed Virgin Mary
With respect to Augustine, there are a couple of possible sources here:
We regard the martyrs with the same affectionate intimacy that we feel towards holy men of God in this life, when we know that their hearts are prepared to endure the same suffering for the truth of the gospel. [...] What is properly divine worship, which the Greeks call latria, and for which there is no word in Latin, both in doctrine and in practice, we give only to God. To this worship belongs the offering of sacrifices; as we see in the word idolatry, which means the giving of this worship to idols. Accordingly we never offer, or require any one to offer, sacrifice to a martyr, or to a holy soul, or to any angel. Any one falling into this error is instructed by doctrine, either in the way of correction or of caution.
From Against Faustus (Contra Faustum), book XX, chapter 21.
St. Augustine also talks about worship that is due to God alone in City of God (emphasis and transliterations mine):
[...] we must now, by God's help, ascertain what is thought about our religious worship and piety by those immortal and blessed spirits, who dwell in the heavenly places among dominations, principalities, powers, whom the Platonists call gods, and some either good demons, or, like us, angels — that is to say, to put it more plainly, whether the angels desire us to offer sacrifice and worship, and to consecrate our possessions and ourselves, to them or only to God, theirs and ours.
For this is the worship which is due to the Divinity, or, to speak more accurately, to the Deity; and, to express this worship in a single word as there does not occur to me any Latin term sufficiently exact, I shall avail myself, whenever necessary, of a Greek word. Λατρεία [latria], whenever it occurs in Scripture, is rendered by the word service. But that service which is due to men, and in reference to which the apostle writes that servants must be subject to their own masters, Ephesians 6:5 is usually designated by another word in Greek, whereas the service which is paid to God alone by worship, is always, or almost always, called λατρεία in the usage of those who wrote from the divine oracles.
[...] [λατρεία], we say, belongs only to that God who is the true God, and who makes His worshippers gods. And therefore, whoever these immortal and blessed inhabitants of heaven be, if they do not love us, and wish us to be blessed, then we ought not to worship them; and if they do love us and desire our happiness, they cannot wish us to be made happy by any other means than they themselves have enjoyed — for how could they wish our blessedness to flow from one source, theirs from another?
It's a bit trickier to find an Augustinian reference to Mary in this way. In On Nature and Grace he does imply that the Virgin Mary may have been sinless, unlike other saints:
Well, then, if, with this exception of the Virgin, we could only assemble together all the forementioned holy men and women, and ask them whether they lived without sin while they were in this life, what can we suppose would be their answer? [...] I put it to you, whether, on having such a question submitted to them, however excellent might have been their sanctity in this body, they would not have exclaimed with one voice: If we say we have no sin, we deceive ourselves, and the truth is not in us? 1 John 1:8
Re: Other Church Fathers' and Mothers' views on the veneration, we have evidence for veneration-like practices at least as early as 155 AD, from the Church of Smyrna (transliterations mine):
Him indeed we adore (προσκυνουμεν) [proskinoumen] as the Son of God; but the martyrs we love as they deserve (αγαπωμεν αξιως) [agapomen axios], for their surpassing love to their King and Master, as we wish also to be their companions and fellow-disciples.
By the fourth century, this was well-established among some of the most famous saints of all time:
In one of his letters, St. Basil explicitly writes that he accepts the intercession of the apostles, prophets and martyrs, and he seeks their prayers to God (Letter 360). Then, speaking about the Forty Martyrs, who suffered martyrdom for Christ, he emphasizes that "they are common friends of the human race, strong ambassadors and collaborators in fervent prayers" (Chapter 8). St. Gregory of Nyssa asks St. Theodore the Martyr "to fervently pray to our Common King, our God, for the country and the people" (Encomium to Martyr Theodore). The same language is used by St. Gregory the Theologian in his encomium to St. Cyprian. St. John Chrysostom says that we should seek the intercession and the fervent prayers of the saints, because they have special "boldness" (parresia), before God. (Gen. 44:2 and Encomium to Julian, Iuventinus and Maximinus, 3).
Here's another bevy of quotations from a Catholic perspective about the intercession of saints.