There is NO such thing as the "Roman Catholic Church".
It is just the "Catholic Church."
I agree. There is just the catholic church.
"Roman" (Latin) refers to ONE of about TWENTY Liturgical Rites that comprise the ONE Catholic Church.
There are Melkite Catholics, Maronites, Byzantines, Coptics and several others - and we are ALL in full communion.
This is the Roman church. All are in submission to the Roman Pontiff are they not?
It is the very SAME Catholic Church that first century Bishop and lifelong student of the Apostle John, Ignatius of Antioch wrote about right before his martyrdom in 107AD.
Ignatius of Antioch
Follow your bishop, every one of you, as obediently as Jesus Christ followed the Father. Obey your clergy too as you would the apostles; give your deacons the same reverence that you would to a command of God. Make sure that no step affecting the Church is ever taken by anyone without the bishop’s sanction. The sole Eucharist you should consider valid is one that is celebrated by the bishop himself, or by some person authorized by him. Where the bishop is to be seen, there let all his people be; just as, wherever Jesus Christ is present, there is the Catholic Church (Letter to the Smyrneans 8:2 [A.D. 107]).
It is the catholic church but he is not a member of a church that won't appear for centuries (ca 700 to 1000 Ad) to come.
But since you brought up Ignatius of Antioch let's take a looksy;
First. lets talk about church offices. Lets start with what the Bible has to say about the matter.
This is why I left you in Crete, so that you might put what remained into order, and appoint elders in every town as I directed you— 6 if anyone is above reproach, the husband of one wife, and his children are believers and not open to the charge of debauchery or insubordination. 7 For an overseer, as God’s steward, must be above reproach. He must not be arrogant or quick-tempered or a drunkard or violent or greedy for gain, 8 but hospitable, a lover of good, self-controlled, upright, holy, and disciplined. 9 He must hold firm to the trustworthy word as taught, so that he may be able to give instruction in sound doctrine and also to rebuke those who contradict it.
The Holy Bible: English Standard Version (Tt 1:5–9). (2016). Crossway Bibles.
The words I have bolded are the Greek words πρεσβύτερος or presbyteros and ἐπίσκοπος or episkapos where we get the word for bishop. The two offices are interchangeable according to Paul. The idea of a monarchial bishop was unknown in the early church so reading the modern Roman idea back into this time is incredibly anachronistic. Historically, there are only two different offices listed that of διάκονος or diakonos where we get the word for Deacon, and ἐπίσκοπος sometimes referred to as πρεσβύτερος.
See that ye all follow the bishop, even as Jesus Christ does the Father, and the presbytery as ye would the apostles; and reverence the deacons, as being the institution of God. Let no man do anything connected with the Church without the bishop. Let that be deemed a proper20 Eucharist, which is [administered] either p 90 by the bishop, or by one to whom he has entrusted it. Wherever the bishop shall appear, there let the multitude [of the people] also be; even as, wherever Jesus Christ is, there is the Catholic Church. It is not lawful without the bishop either to baptize or to celebrate a love-feast; but whatsoever he shall approve of, that is also pleasing to God, so that everything that is done may be secure and valid.
Ignatius of Antioch. (1885).
The Epistle of Ignatius to the Smyrnæans. In A. Roberts, J. Donaldson, & A. C. Coxe (Eds.),
The Apostolic Fathers with Justin Martyr and Irenaeus (Vol. 1, pp. 89–90). Christian Literature Company.
The word that your translation used for πρεσβυτερίῳ is clergy but the better translation would be presbytery or group of elders. You see, the bishop or episkapos is just one of the elders in church. I included the original Greek text if you would like to look it up for yourself.
Τοὺς δὲ μερισμοὺς φεύγετε, ὡς ἀρχὴν κακῶν. Πάντες τῷ ἐπισκόπῳ ἀκολουθεῖτε, ὡς Ἰησοῦς Χριστὸς τῷ Πατρί· καὶ τῷ πρεσβυτερίῳ, ὡς τοῖς ἀποστόλοις· τοὺς δὲ διακόνους ἐντρέπεσθε, ὡς Θεοῦ ἐντολήν. Μηδεὶς χωρὶς τοῦ ἐπισκόπου τὶ πρασσέτω τῶν ἀνηκόντων εἰς τὴν ἐκκλησίαν. Ἐκείνη βεβαία εὐχαριστία ἡγείσθω, ἡ ὑπὸ τὸν ἐπίσκοπον οὖσα, ἢ ᾧ ἂν αὐτὸς ἐπιτρέψῃ. Ὅπου ἂν φανῇ ὁ ἐπίσκοπος, ἐκεῖ τὸ πλῆθος ἔστω, ὥσπερ ὅπου ἂν ᾖ Χριστὸς [Ἰησοῦς, ἐκεῖ ἡ καθολικὴ ἐκκλησία.] Οὐκ ἐξόν ἐστιν χωρὶς τοῦ ἐπισκόπου οὔτε βαπτίζειν, οὔτε ἀγάπην ποιεῖν· ἀλλʼ ὃ ἂν ἐκεῖνος δοκιμάσῃ, τοῦτο καὶ τῷ Θεῷ εὐάρεστον, ἵνʼ ἀσφαλὲς ᾖ καὶ βέβαιον πᾶν ὃ πράσσεται.
Ignatius of Antioch. (1849).
Corpus Ignatianum: Greek Text, Middle Recension (W. Cureton, Trans.; p. 109). Asher and Co.
So you see that text doesn't really help you as you could easily say "Pastor" instead of bishop. The bishop in this case is not in charge or a diocese as the Roman Empire had yet to experience the Diocletian reforms (fourth centuty AD). He's a pastor or elder or overseer (one of several) in the local church. That is why your use of Ignatius is improper and anachronistic.
A.