Purgatory

The Early Church Fathers

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St. Augustine
Temporary punishments are suffered by some in this life only, by others after death, by others both now and then; but all of them before that last and strictest judgment. But of those who suffer temporary punishments after death, all are not doomed to those everlasting pains which are to follow that judgment.
The City of God, Book 21, Chapter 13

St. Augustine
In the books of the Maccabees we read of sacrifice offered for the dead. Even if it were nowhere at all read in the Old Scriptures, not small is the authority, which in this usage is clear¸ of the whole Church, namely that in the prayers of the priest which are offered to the Lord God at His Altar, the commendation of the dead has also its place.
On Care to be had for the Dead, Chapter 1:3

St. John Chrysostom
Weep for the unbelievers; weep for those who differ in nowise from them, those who depart hence without the illumination, without the seal! They indeed deserve our wailing, they deserve our groans; they are outside the Palace, with the culprits, with the condemned: for ‘Verily I say unto you, except a man be born of water and the Spirit, he shall not enter into the kingdom of Heaven’ (John 3:5). Mourn for those who have died in wealth and did not from their wealth think of any solace for their soul, who had power to wash away their sins and would not…Let us weep for these; let us assist them according to our power; let us think of some assistance for them¸ small though it be, yet still let us assist them. How and in what way? By praying and entreating others to make prayers for them, by continually giving to the poor on their behalf…Not in vain did the Apostles order that remembrance should be made of the dead in the dreadful Mysteries. They know that great gain results to them, great benefit; for when the whole people stands with uplifted hands, a priestly assembly, and that awful Sacrifice lies displayed, how shall we not prevail with God by our entreaties for them. And this we do for those who have departed in faith.
Homilies on Philippians, 3:4