“The term cathedra was applied also to the see of a bishop. The **earliest use of the word in this sense occurs in Tertullian (c 200 AD), **who speaks (De praescriptione, XXXVI) of “cathedrae Apostolorum” in allusion to Apostolic succession in episcopal sees.” -“Cathedra” in NewAdvent
“The Church of God which sojourns in Rome to the Church of God which sojourns in Corinth…If anyone disobey the things which have been said by Him through us, let them know that they will involve themselves in transgression and in no small danger.”
Pope Clement of Rome [regn. c A.D.91-101], 1st Epistle to the Corinthians, 1,59:1 (c. A.D. 96).
“Thereupon Victor, who presided over the church at Rome, immediately attempted to cut off from the common unity the parishes of all Asia, with the churches that agreed with them, as heterodox; and he wrote letters and declared all the brethren there wholly excommunicate…”
Pope Victor I [regn. A.D. 189-198], in Eusebius EH, 24:9 (A.D. 192).
“Stephen, that he who so boasts of the place of his episcopate, and contends that he holds the succession from Peter, on whom the foundations of the Church were laid…Stephen, who announces that he holds by succession the throne of Peter.”
Pope Stephen I [regn. A.D. 254-257], Firmilian to Cyprian, Epistle 74/75:17 (A.D. 256).
“I beseech you, readily bear with me: what I write is for the common good. For what we have received from the blessed Apostle Peter s, that I signify to you; and I should not have written this, as deeming that these things were manifest unto all men, had not these proceedings so disturbed us.” *Pope Julius [regn. A.D. 337-352], To the Eusebians, fragment in Athanasius’ Against the Arians, 2:35 (c. A.D. 345). *
“Why then do you again ask me for the condemnation of Timotheus? Here, by the judgment of the apostolic see, in the presence of Peter, bishop of Alexandria, he was condemned, together with his teacher, Apollinarius, who will also in the day of judgment undergo due punishment and torment. But if he succeeds in persuading some less stable men, as though having some hope, after by his confession changing the true hope which is in Christ, with him shall likewise perish whoever of set purpose withstands the order of the Church. May God keep you sound, most honoured sons.” *Pope Damasus [regn. A.D. 366-384], To the Eastern Bishops, fragment in Theodoret’s EH, 5:10 (c. A.D. 372). *
“We bear the burdens of all who are heavy laden; nay, rather, the blessed apostle Peter bears them in us and protects and watches over us, his heirs, as we trust, in all the care of his ministry…Now let all your priests observe the rule here given, unless they wish to be plucked from the solid, apostolic rock upon which Christ built the universal Church…I think, dearest brother, disposed of all the questions which were contained in your letter of inquiry and have, I believe, returned adequate answers to each of the cases you reported by our son, the priest Basianus, to the Roman Church as to the head of your body…And whereas no priest of the Lord is free to be ignorant of the statutes of the Apostolic See and the venerable provisions of the canons.” *Pope Sircius [regn. c A.D. 384-399], To Himerius, bishop of Tarragona (Spain), 1,3,20 (c. A.D. 392). *
“Care shall not be lacking on my part to guard the faith of the Gospel as regards my peoples, and to visit by letter, as far as I am able, the parts of my body throughout the divers regions of the earth.” *Pope Anastasius [regn. A.D. 399-401], Epistle 1 (c. A.D. 400). *
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http://www.scripturecatholic.com/primacy_of_peter.html#tradition_III
Primacy of Peter’s Apostolic See
“Ignatius, who is also called Theophorus, to the Church which has obtained mercy, through the majesty of the Mast High God the Father, and of Jesus Christ, His only-begotten Son; the Church which is sanctified and enlightened by the will of God, who farmed all things that are according to the faith and love of Jesus Christ, our God and Saviour; the Church which presides in the place of the region of the Romans, and which is worthy of God, worthy of honour, worthy of the highest happiness, worthy of praise, worthy of credit, worthy of being deemed holy, and which presides over love…”
Ignatius of Antioch, Epistle to the Romans, Prologue (A.D. 110).
"There is extant also another epistle written by Dionysius to the Romans, and addressed to Soter, who was bishop at that time. We cannot do better than to subjoin some passages from this epistle…In this same epistle he makes mention also of Clement’s epistle to the Corinthians, showing that it had been the custom from the beginning to read it in the church. His words are as follows: To-day we have passed the Lord’s holy day, in which we have read your epistle. From it, whenever we read it, we shall always be able to draw advice, as also from the former epistle, which was written to us through Clement.’
Dionysius of Corinth, To Pope Soter (A.D. 171).
“Since, however, it would be very tedious, in such a volume as this, to reckon up the successions of all the Churches, we do put to confusion all those who, in whatever manner, whether by an evil self-pleasing, by vainglory, or by blindness and perverse opinion, assemble in unauthorized meetings; [we do this, I say,] by indicating that tradition derived from the apostles, of the very great, the very ancient, and universally known Church founded and organized at Rome by the two most glorious apostles, Peter and Paul; as also [by pointing out] the faith preached to men, which comes down to our time by means of the successions of the bishops. For it is a matter of necessity that every Church should agree with this Church, on account of its pre- eminent authority, that is, the faithful everywhere, inasmuch as the apostolical tradition has been preserved continuously by those [faithful men] who exist everywhere.”
Irenaeus, Against Heresies, 3:3:2 (A.D. 180).
Continued at;
Rome may think they have held multiple councils after the first seven. But they are not true Ecumenical Councils.