I recently read "The Early Papacy" by Adrian Fortescue. There are four points which Adrian makes, which are supported by various writings of Church "fathers" from 100 to 451 AD:
1. The Bishop of Rome (the pope) was considered the chief bishop of the early Church.
2. The pope had jurisdiction over other bishops in the Church.
3. To be a member of the Church, one had to be in communion with the pope.
4. The early Church believed that God's providence would prevent the Church, and therefore the pope, from errors in his teaching.
Mr. Fortescue quotes from Ignatius, Irenaeus, Clement, Justin Martyr, (2nd century), Cyprian (3rd century), who, in various surviving writings, supported these claims.
If you are interested in the Catholic argument for papal primacy, (either to argue for it or against it), then I highly recommend the book.
Hope this helps,
Jonathan
