The denials of Peter
Whether the rooster crowed once, as Matthew, Luke and John record Jesus saying, or twice, as Mark does, and how John's three denials map onto the accounts.
Matthew 26:69-75
69Now Peter was sitting outside in the court, and a maid came to him, saying, “You were also with Jesus, the Galilean!”
70But he denied it before them all, saying, “I don’t know what you are talking about.”
71When he had gone out onto the porch, someone else saw him, and said to those who were there, “This man also was with Jesus of Nazareth.”
72Again he denied it with an oath, “I don’t know the man.”
73After a little while those who stood by came and said to Peter, “Surely you are also one of them, for your speech makes you known.”
74Then he began to curse and to swear, “I don’t know the man!” Immediately the rooster crowed.
75Peter remembered the word which Jesus had said to him, “Before the rooster crows, you will deny me three times.” Then he went out and wept bitterly.
John 18:15-27
15Simon Peter followed Jesus, as did another disciple. Now that disciple was known to the high priest, and entered in with Jesus into the court of the high priest;
16but Peter was standing at the door outside. So the other disciple, who was known to the high priest, went out and spoke to her who kept the door, and brought in Peter.
17Then the maid who kept the door said to Peter, “Are you also one of this man’s disciples?” He said, “I am not.”
18Now the servants and the officers were standing there, having made a fire of coals, for it was cold. They were warming themselves. Peter was with them, standing and warming himself.
19The high priest therefore asked Jesus about his disciples and about his teaching.
20Jesus answered him, “I spoke openly to the world. I always taught in synagogues, and in the temple, where the Jews always meet. I said nothing in secret.
21Why do you ask me? Ask those who have heard me what I said to them. Behold, they know the things which I said.”
22When he had said this, one of the officers standing by slapped Jesus with his hand, saying, “Do you answer the high priest like that?”
23Jesus answered him, “If I have spoken evil, testify of the evil; but if well, why do you beat me?”
24Annas sent him bound to Caiaphas, the high priest.
25Now Simon Peter was standing and warming himself. They said therefore to him, “You aren’t also one of his disciples, are you?” He denied it and said, “I am not.”
26One of the servants of the high priest, being a relative of him whose ear Peter had cut off, said, “Didn’t I see you in the garden with him?”
27Peter therefore denied it again, and immediately the rooster crowed.
What each tradition says
Rabbinic / Midrashic
No sourced position found. Checked the Jewish Encyclopedia (1905), articles "Simon Cephas" (no mention of the denials), "Jesus of Nazareth" and "New Testament"; Sefaria holds no Gospel text. No rabbinic position on the number of cock-crowings found.
Patristic
Augustine says that as regards Peter’s actual spoken denials, the threefold denial was entered upon before the first cockcrow and finished before the second. Yet as regards Peter’s disposition of mind and apprehensions, it was conceived as a whole before the first cockcrow.
Augustine, Harmony of the Gospels (Nicene and Post-Nicene Fathers, First Series, Vol. 6; S.D.F. Salmond trans.) — Book III, ch. 2 (§7)
Catholic
Haydock says St. Mark is more particular: “before the cock crow twice, thou shalt deny me thrice.” The sense seems to be that this refers to the time before the cock crows the second time, toward morning.
George Leo Haydock, George Haydock's Catholic Bible Commentary (1859) — On Matthew 26:34
Orthodox
No sourced position found. Checked archive.org for a public-domain English Theophylact or Euthymius Zigabenus Gospel commentary (none); Philaret’s Longer Catechism and the Acts of the Synod of Jerusalem (dogmatic texts, no narrative harmonization); pravoslavieto.com (no English commentary on Matthew 26). No Eastern treatment of the cock-crowing count found.
Reformed / Protestant
Calvin says Matthew, Luke, and John report that Peter denied our Lord three times before the cock-crowing ended. Mark states more distinctly that within a short time Peter reached the third denial and, though warned by the first crowing, did not repent.
John Calvin, Commentary on a Harmony of the Evangelists, Matthew, Mark, and Luke, Vol. 3 (Calvin Translation Society, 1846) — On Matthew 26:34 / Mark 14:30-72
Evangelical
John Wesley takes “before cock crowing” in Matthew 26:34 to mean before three in the morning, the usual time for cock crowing. He adds that one cock was heard to crow once after Peter’s first denial of his Lord.
John Wesley, Explanatory Notes upon the New Testament — Note on Matthew 26:34