The Didache tells Christians gathering on the Lord’s Day to confess their transgressions so that their offering may be pure (Didache 14). Tertullian describes exomologesis as an outward discipline in which penitents bow before presbyters and ask the brethren’s prayers (On Repentance 9–10). Cyprian’s correspondence and later canons show bishops and presbyters overseeing exclusion, penance, and reconciliation.
This does not mean that ancient practice looked exactly like a modern private confession. Public penance could be severe, and the disclosure of particular sins varied. The historical point is narrower: the Fathers did not imagine post-baptismal repentance as wholly detached from the Church’s prayer, discipline, and authorized ministry.
Primary sources
Didache 14: https://www.newadvent.org/fathers/0714.htm
Tertullian, On Repentance 9–10: https://www.newadvent.org/fathers/0320.htm
Apostolic Constitutions, Book II: https://www.newadvent.org/fathers/07152.htm