Did any of the Early Church Fathers use the Orthodox canon?

The answer is no, but we should also understand that no early church Fathers used the Roman Catholic canon either. The first time we know of all the current New Testament books being listed anywhere was the Festal Letter of Athanasius in 367 a.d.

Again it is not tedious to speak of the [books] of the New Testament. These are, the four Gospels, according to Matthew, Mark, Luke, and John. Afterwards, the Acts of the Apostles and Epistles (called Catholic), seven, viz. of James, one; of Peter, two; of John, three; after these, one of Jude. In addition, there are fourteen Epistles of Paul, written in this order. The first, to the Romans; then two to the Corinthians; after these, to the Galatians; next, to the Ephesians; then to the Philippians; then to the Colossians; after these, two to the Thessalonians, and that to the Hebrews; and again, two to Timothy; one to Titus; and lastly, that to Philemon. And besides, the Revelation of John.

Athanasius' list of OT books is quite close to the Jewish and Protestant lists. However, he adds the Book of Baruch and the Letter of Jeremiah, and he excludes the Book of Esther.

There are, then, of the Old Testament, twenty-two books in number; for, as I have heard, it is handed down that this is the number of the letters among the Hebrews; their respective order and names being as follows. The first is Genesis, then Exodus, next Leviticus, after that Numbers, and then Deuteronomy. Following these there is Joshua, the son of Nun, then Judges, then Ruth. And again, after these four books of Kings, the first and second being reckoned as one book, and so likewise the third and fourth as one book. And again, the first and second of the Chronicles are reckoned as one book. Again Ezra, the first and second are similarly one book. After these there is the book of Psalms, then the Proverbs, next Ecclesiastes, and the Song of Songs. Job follows, then the Prophets, the twelve being reckoned as one book. Then Isaiah, one book, then Jeremiah with Baruch, Lamentations, and the epistle, one book; afterwards, Ezekiel and Daniel, each one book.

So the answer is no. No early church Father used the Orthodox Canon. Nor is there solid evident that they used what would become the Catholic or Protestant versions either. Athanasius was the first to list what eventually became the New Testament books, and he came close to the Protestant and Jewish versions of the OT. Since this came well after the Council of Nicaea, it should probably not be considered part of "Early Church" in my opinion.

Being one of the only Eastern Catholic saints I know St. Gregory of Nazianzus (4th century, so on the upper end of the spectrum) references something that is technically (there weren't chapters in those days) in the 38th chapter of 2nd Chronicles.

https://www.newadvent.org/fathers/310239.htm

and this one is far more august than all the others, inasmuch as it cannot be defiled by after-stains. Yes, and I know of a Fifth also, which is that of tears, and is much more laborious, received by him who washes his bed every night and his couch with tears; whose bruises stink through his wickedness; and who goes mourning and of a sad countenance; who imitates the repentance of Manasseh 2 Chronicles 38:12

I think that might be a misprint and they meant 2 Chronichles:33 (3's being easy to OCR into 8's when you're not paying attention)

But even 2 Chronicles:33 doesn't really talk about Manasseh's repentance, especially not as much as the Prayer of Manasseh, which is in the Orthodox Canon and clearly referenced as something that was kept somewhere (Except not in the scriptures for some reason unbeknownst to me)

I think it's reasonable to think that St. Gregory was referring to the prayer itself rather than the account in Chronicles and therefore an example of a Church father referencing the Orthodox canon.