Sounds like the early church believed the Church Christ established was called “Catholic”…“the pillar and bulwark of truth”. Just wrote this on another post.
See that ye all follow the bishop, even as Christ Jesus does the Father, and the presbytery as ye would the apostles. Do ye also reverence the deacons, as those that carry out the appointment of God. Let no man do anything connected with the Church without the bishop. Let that be deemed a proper Eucharist, which is [administered] either by the bishop, or by one to whom he has entrusted it. Wherever the bishop shall appear, there let the multitude also be; by the bishop, or by one to whom he has entrusted it. Wherever the bishop shall appear, there let the multitude also be; even as, **wherever Jesus Christ is, there is the Catholic Church." **Ignatius of Antioch, Epistle to the Smyrneans, 8:2 (c. A.D. 110).
And then there was Irenaeus…
“[N]or does it consist in this, that he should again falsely imagine, as being above this [fancied being], a Pleroma at one time supposed to contain thirty, and at another time an innumerable tribe of Aeons, as these teachers who are destitute of truly divine wisdom maintain;
while the Catholic Church possesses one and the same faith throughout the whole world, as we have already said.” Irenaeus, Against Heresies, 1:10,3 (A.D. 180).
What other church are you thinking or believing of if not Catholic and which of the early church fathers write about it?