Firmilian, Bishop of Caesarea in Cappadocia (A.D. 256) - Epistle LXXIV To Cyprian, Against the Letter of Stephen:

(7) "Moreover, all other heretics, if they have separated themselves from the Church of God, can have nothing of power or of grace, since all power and grace are established in the Church where the elders preside, who possess the power both of baptizing, and of imposition of hands, and of ordaining. For as a heretic may not lawfully ordain nor lay on hands, so neither may he baptize, nor do any thing holily or spiritually, since he is an alien from spiritual and deifying sanctity.

(14) "But if the spouse of Christ is one, which is the Catholic Church, it is she herself who alone bears sons of God. For there are not many spouses of Christ"

(16) "But what is the greatness of his error, and what the depth of his blindness, who says that remission of sins can be granted in the synagogues of heretics, and does not abide on the foundation of the one Church which was once based by Christ upon the rock, may be perceived from this, that Christ said to Peter alone, "Whatsoever thou shall bind on earth shall be bound in heaven, and whatsoever thou shall loose on earth shall be loosed in heaven." And again, in the Gospel, when Christ breathed on the apostles alone, saying, "Receive ye the Holy Ghost: whose soever sins ye remit they are remitted unto them, and whose soever sins ye retain they are retained." Therefore the power of remitting sins was given to the apostles, and to the churches which they, sent by Christ, established, and to the bishops who succeeded to them by vicarious ordination. But the enemies of the one Catholic Church in which we are, and the adversaries of us who have succeeded the apostles, asserting for themselves, in opposition to us, unlawful priesthoods, and setting up profane altars, what else are they than Korah, Dathan, and Abiram, profane with a like wickedness, and about to suffer the same punishments which they did, as well as those who agree with them, just as their partners and abettors perished with a like death to theirs?"

Tertullian (A.D. 200) - The Demurrer Against the Heretics

CHAP.XXXII.—NONE OF THE HERETICS CLAIM SUCCESSION FROM THE APOSTLES. NEW CHURCHES STILL APOSTOLIC, BECAUSE THEIR FAITH IS THAT WHICH THE APOSTLES TAUGHT AND HANDED DOWN. THE HERETICS CHALLENGED TO SHOW ANY APOSTOLIC CREDENTIALS.:

"Let them produce the original records of their churches; let them unfold the roll of their bishops, running down in due succession from the beginning in such a manner that [that first bishop of theirs] bishop shall be able to show for his ordainer and predecessor some one of the apostles or of apostolic men,—a man, moreover, who continued stedfast with the apostles. For this is the manner in which the apostolic churches transmit their registers: as the church of Smyrna, which records that Polycarp was placed therein by John; as also the church of Rome, which makes Clement to have been ordained in like manner by Peter."

St. Irenaeus (A.D. 180-199) - Against Heresies

BOOK III, CHAP.III.1 -- A REFUTATION OF THE HERETICS, FROM THE FACT THAT, IN THE VARIOUS CHURCHES, A PERPETUAL SUCCESSION OF BISHOPS WAS KEPT UP.:

"We are in a position to reckon up those who were by the apostles instituted bishops in the Churches, and [to demonstrate] the succession of these men to our own times...For if the apostles had known hidden mysteries, which they were in the habit of imparting to "the perfect" apart and privily from the rest, they would have delivered them especially to those to whom they were also committing the Churches themselves. For they were desirous that these men should be very perfect and blameless in all things, whom also they were leaving behind as their successors, delivering up their own place of government to these men; which men, if they discharged their functions honestly, would be a great boon [to the Church], but if they should fall away, the direst calamity."

St. Irenaeus (A.D. 180-199) - Against Heresies

BOOK III, CHAP. III.--A REFUTATION OF THE HERETICS, FROM THE FACT THAT, IN THE VARIOUS CHURCHES, A PERPETUAL SUCCESSION OF BISHOPS WAS KEPT UP.:

"[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"

St. Irenaeus (A.D. 180-199) - Against Heresies

BOOK III, CHAP. II:2-3:—THE HERETICS FOLLOW NEITHER SCRIPTURE NOR TRADITION.:

"2. But, again, when we refer them to that tradition which originates from the apostles, [and] which is preserved by means of the succession of presbyters in the Churches, they object to tradition, saying that they themselves are wiser not merely than the presbyters, but even than the apostles, because they have discovered the unadulterated truth. For [they maintain] that the apostles intermingled the things of the law with the words of the Saviour; . . . but that they themselves, indubitably, unsulliedly, and purely, have knowledge of the hidden mystery: this is, indeed, to blaspheme their Creator after a most impudent manner! It comes to this, therefore, that these men do now consent neither to Scripture nor to tradition.

3. Such are the adversaries with whom we have to deal, my very dear friend, endeavouring like slippery serpents to escape at all points. Where- fore they must be opposed at all points, if per- chance, by cutting off their retreat, we may succeed in turning them back to the truth. For, though it is not an easy thing for a soul under the influence of error to repent, yet, on the other hand, it is not altogether impossible to escape from error when the truth is brought alongside it."