Fidelity to Church tradition, even in the slightest thing, is critical

We are obedient to you, O King, in things concerning our daily life, in tributes, taxes, and payments, which are your due; but in ecclesiastical government we have our pastors, preachers of the word, and exponents of ecclesiastical law. We do not change the boundaries marked out by our fathers (Prov. 22.28): we keep the tradition we have received. If we begin to lay down the law to the Church, even in the smallest thing, the whole edifice will fall to the ground in no short time.

St. John Damascene
Apology Against Those Who Decry Holy Images
Part II

Unwritten traditions are handed down in the Church

How do we know the Holy place of Calvary, or the Holy Sepulchre? Does it not rest on a tradition handed down from father to son? It is written that our Lord was crucified on Calvary, and buried in a tomb, which Joseph hewed out of the rock; (Mt. 27.60) but it is unwritten tradition which identifies these spots, and does more things of the same kind. Whence come the three immersions at baptism, praying with face turned towards the east, and the tradition of the mysteries?* Hence St Paul says, “Therefore, brethren, stand fast, and hold the traditions which you have learned either by word, or by our epistle.” (II Thess. 2.15) As, then, so much has been handed down in the Church, and is observed down to the present day, why disparage images?

St. John Damascene
Apology Against Those Who Decry Holy Images
Part I

Apostolic tradition “alone” is the source of authority

…as the teaching of the Church, transmitted in orderly succession from the Apostles, and remaining in the Churches to the present day, is still preserved, that alone is to be accepted as truth which differs in no respect from ecclesiastical and apostolical tradition.

Origen
On First Principles, Book I
Preface

Peter and Paul were martyred in Rome

We read the lives of the Cæsars: At Rome Nero was the first who stained with blood the rising faith. Then is Peter girt by another, when he is made fast to the cross. Then does Paul obtain a birth suited to Roman citizenship, when in Rome he springs to life again ennobled by martyrdom.  Wherever I read of these occurrences, so soon as I do so, I learn to suffer; nor does it signify to me which I follow as teachers of martyrdom, whether the declarations or the deaths of the apostles, save that in their deaths I recall their declarations also.

Tertullian
Scorpiace
Chapter XV

The Lord gave the keys to heaven to Peter, then to the Church, then to every believer

For though you think heaven still shut, remember that the Lord left here to Peter and through him to the Church, the keys of it, which every one who has been here put to the question, and also made confession, will carry with him.

Tertullian
Scorpiace
Chapter X

The doctrine of God came from the Apostles

Some disputed about eating idol sacrifices, others about the veiled dress of women, others again about marriage and divorce, and some even about the hope of the resurrection; but about God no one disputed. Now, if this question also had entered into dispute, surely it would be found in the apostle, and that too as a great and vital point. No doubt, after the time of the apostles, the truth respecting the belief of God suffered corruption, but it is equally certain that during the life of the apostles their teaching on this great article did not suffer at all; so that no other teaching will have the right of being received as apostolic than that which is at the present day proclaimed in the churches of apostolic foundation.

…Show us, then, one of your churches, tracing its descent from an apostle, and you will have gained the day.

Tertullian
The Five Books Against Marcion, Book I
Chapter XXI

Martyrdom of the Apostles and the core of their teaching

Come now, you who would indulge a better curiosity, if you would apply it to the business of your salvation, run over the apostolic churches, in which the very thrones of the apostles are still pre-eminent in their places, in which their own authentic writings are read, uttering the voice and representing the face of each of them severally. Achaia is very near you, (in which) you find Corinth. Since you are not far from Macedonia, you have Philippi; (and there too) you have the Thessalonians. Since you are able to cross to Asia, you get Ephesus. Since, moreover, you are close upon Italy, you have Rome, from which there comes even into our own hands the very authority (of apostles themselves). How happy is its church, on which apostles poured forth all their doctrine along with their blood! where Peter endures a passion like his Lord’s! where Paul wins his crown in a death like John’s where the Apostle John was first plunged, unhurt, into boiling oil, and thence remitted to his island-exile! See what she has learned, what taught, what fellowship has had with even (our) churches in Africa! One Lord God does she acknowledge, the Creator of the universe, and Christ Jesus (born) of the Virgin Mary, the Son of God the Creator; and the Resurrection of the flesh; the law and the prophets she unites in one volume with the writings of evangelists and apostles, from which she drinks in her faith. This she seals with the water (of baptism), arrays with the Holy Ghost, feeds with the Eucharist, cheers with martyrdom, and against such a discipline thus (maintained) she admits no gainsayer.

Tertullian
Against Marcion
The Prescription Against Heretics
Chapter XXXVI

Heretics must prove that the orthodox lack continuity with the Apostolic faith

…since they deny the truth of (our doctrine), they ought to prove that it also is heresy, refutable by the same rule as that by which they are themselves refuted; and at the same time to show us where we must seek the truth, which it is by this time evident has no existence amongst them.  Our system is not behind any in date; on the contrary, it is earlier than all; and this fact will be the evidence of that truth which everywhere occupies the first place.

Tertullian
Against Marcion
The Prescription Against Heretics
Chapter XXXV

If the heretic’s faith is true, let him prove it by a record of Apostolic succession and full-communion status

But if there be any (heresies) which are bold enough to plant themselves in the midst of the apostolic age, that they may thereby seem to have been handed down by the apostles, because they existed in the time of the apostles, we can say: 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. In exactly the same way the other churches likewise exhibit (their several worthies), whom, as having been appointed to their episcopal places by apostles, they regard as transmitters of the apostolic seed. Let the heretics contrive something of the same kind.

….To this test, therefore will they be submitted for proof by those churches, who, although they derive not their founder from apostles or apostolic men (as being of much later date, for they are in fact being founded daily), yet, since they agree in the same faith, they are accounted as not less apostolic because they are akin in doctrine. Then let all the heresies, when challenged to these two tests by our apostolic church, offer their proof of how they deem themselves to be apostolic. But in truth they neither are so, nor are they able to prove themselves to be what they are not. Nor are they admitted to peaceful relations and communion by such churches as are in any way connected with apostles, inasmuch as they are in no sense themselves apostolic because of their diversity as to the mysteries of the faith.

Tertullian
Against Marcion
The Prescription Against Heretics
Chapter XXXII