There is a distinction to be recognized between 'Eternal Security', which rests it's hope in what God has promised to do for us in Christ, and 'Assurance of Salvation', which is personally realized as the life mirrors the confession. The writings of the Early Church Fathers were not theological dissections of terms and doctrines but, rather, they were largely exhortations to live out that which comes from and demonstrates salvation.
Those who are particular about words, and devote their time to them, miss the point of the whole picture (Clement of Alexandria, The Stromata, Bk. II, Ch. 1, AD 150-215)
For this reason it is difficult to find any direct exposition of something that sounds like Once Saved Always Saved as we hear it presented nowadays. If this teaching is something that was understood, it will be revealed best in topics of practical application. Much like John's first epistle, which is filled with exhortation to BE what is claimed and filled with warning that fruitless life proves the claim to faith is a lie, assurance is gained when the fruits of genuine salvation are manifested:
I write these things to you who believe in the name of the Son of God, that you may know that you have eternal life. - 1 John 5:13
And to what things is John here referring? The entire epistle contrasts behavior that demonstrates the truth of claiming to be in Christ with behavior that proves the claim of faith to be a lie. The entire epistle establishes actual saving union with Christ as the ground and wellspring of righteous behavior rather than the means to it. That is to say: A right understanding of genuine Assurance assumes Eternal Security.
There is a tension that is sometimes assumed in Scripture between Paul (Abraham justified by faith) and James (Abraham justified by works) but that tension disappears when we recognize that a distinction exists between justification of our sinful selves before God by Christ and justification/demonstration of our faith before men through actions (see James below). Paul clearly makes the distinction at the outset of his discussion:
For if Abraham was justified by works, he has something to boast about, but not before God. - Romans 4:2
And James does as well, assuming the primacy of faith as per Paul and making practical application:
Show me your faith apart from your works, and I will show you my faith by my works. - James 2:18b
The early Church Fathers almost unanimously came at this from James' position of assuming justification before God solely based upon what God has done in Christ, insisting that faith in Christ produces a new life, and encouraging believers to be diligent in manifesting the faith. Clement's first letter (~AD 97) is the earliest Christian document outside the NT and in it we find this same 'tension':
And we, therefore…are not justified of ourselves or by our wisdom or insight or religious devotion or the holy deeds we have done from the heart, but by that faith by which almighty God has justified all men from the very beginning (ch. 32:4).
We should clothe ourselves with concord, being humble,
self-controlled, far removed from all gossiping and slandering, and
justified by our deeds, not by words (ch. 30:3).
Ignatius of Antioch also displays the same theological 'tension' regarding works as is found in Scripture:
Let your baptism be ever your shield, your faith a helmet, your charity a spear, your patience a panoply. Let your works be deposits, so that you may receive the sum that is due you” (Letter to St. Polycarp, 6).
Therefore, let us not be ungrateful for His kindness. For if He were to reward us according to our works, we would cease to be (Epistle to the Magnesians, Ch. 5).
Justin Martyr approaches the issue of personal assurance from the same assumption that Christian behavior is sourced in the eternal reality of the new birth:
Those who are found not living as he taught should know that they are not really Christians, even if his teachings are on their lips, for he said that not those who merely profess but those who also do the works will be saved (cf. Matt. 13:42, 43; 7:15,16,19)” (The First Apology of Justin, ch.16).
The clear implication in this statement is that those who really are Christians will be found living as He taught. Thus Justin Martyr places the source of 'Assurance of our Salvation' squarely in the realm of 'Eternal Security' just as Jesus taught.
Jesus answered them, “I told you, and you do not believe. The works that I do in my Father's name bear witness about me, but you do not believe because you are not among my sheep. My sheep hear my voice, and I know them, and they follow me. I give them eternal life, and they will never perish, and no one will snatch them out of my hand. My Father, who has given them to me, is greater than all, and no one is able to snatch them out of the Father's hand. I and the Father are one.” - John 10:25-30
Thus, Augustine was not inventing something new when he said, regarding perseverance
We do the works, but God works in us the doing of the works (De Dono
Perseverentiae, 13, 33)
he was merely reiterating what was taught by Jesus and expounded upon by Paul; When we are born again, by grace through faith, we receive the Holy Spirit as a deposit guaranteeing our inheritance and the life going forward is God working in us both to will and to do His good pleasure (Philippians 2:13). God was in them and would never leave nor forsake them (eternal security) but would, rather, complete the good work that was begun in them.
Tertullian echoes the same:
We make petition, then, that He supply us with the substance of His will and the capacity to do it–so that we may be saved both in the heaven and on earth (On Prayer, part III, ch. IV).
The Security of Salvation once received by faith was so fundamentally assumed in the early church that they barely needed to address it directly. Instead they focused on that which constituted the demonstration of that truth. A claim is easy to make and it is the demonstration that proves the claim is already true.
But Jesus, knowing their thoughts, said, “Why do you think evil in your hearts? For which is easier, to say, ‘Your sins are forgiven,’ or to say, ‘Rise and walk’? But that you may know that the Son of Man has authority on earth to forgive sins”—he then said to the paralytic—“Rise, pick up your bed and go home.” - Matthew 9:4-6