Is there any tradition about Jesus' appearance to Simon Peter?

According to Paul in 1 Corinthians. 15:

I delivered unto you first of all that which I also received, how that Christ... was seen of Cephas [Aramaic for "Peter"], then of the twelve...

So Peter's meeting with Jesus happened before Jesus appeared to the disciples collectively.

Luke 24 relates how Jesus met two of his followers traveling to Emmaus and:

•  
• 24:30 took bread, and blessed it, and brake, and gave to them.
• 24:31 And their eyes were opened, and they knew him; and he vanished out of their sight.
• ...
• 24:33 And they rose up the same hour, and returned to Jerusalem, and found the eleven gathered together and them that were with them,
• 24:34 Saying, The Lord is risen indeed, and hath appeared to Simon [Peter].
• 24:35 And they told what things were done in the way, and how he was known of them in breaking of bread.

That is, the two travelers, on their return, reported to the disciples gathered in the room that Simon Peter had seen Jesus. There are two reasons to think that this was the travelers' report, and not the disciples' report.

First, grammatically the use of a comma between "them" (the eleven) and "saying" means that the eleven were not the ones who were speaking. For example, "Thomas shouted at Bob, running in the water" means that Thomas was running in the water, because the comma removes the verb "saying" from the noun immediately preceding it (Bob).

Alternately, "John gave the letter to the postman walking down the street" means that it was the postman who was walking, because no common is used.

In this case, the travelers "found the eleven gathered and them that were with them (the eleven), saying" that Jesus appeared to Peter.

Καὶ ἀναστάνεὗρον συνηθροισμένους τοὺς ἕνδεκα καὶ τοὺς σὺν αὐτοῖς,

...they found gathered together the eleven and those with them,

λέγοντας ὅτι Ἠγέρθη ὁ κύριος ὄντως, καὶ ὤφθη Σίμωνι.

saying indeed has risen the Lord.

Secondly, in Mark 16:9-16, it says that the disciples gathered in Jerusalem did not believe the reports that the women and the two travelers had seen Jesus, and then Jesus showed up and rebuked the disciples for their unbelief. This unbelief would contradict an idea that in Luke 24 it was the eleven disciples who announced affirmatively to the travelers that Simon Peter had actually seen Jesus.

If the travelers had announced to those already assembled that Peter had seen Jesus, then where was Peter? He wouldn't have been one of the two travelers, since Luke says that both travelers had seen Jesus, not just one of them. And he wouldn't be among the rest of those gathered, because it would not make sense for the two travelers to announce on arrival to Peter and the others that Peter had seen Jesus.

Maybe he was over in Galilee with the apostle Thomas? In John 16:32, Jesus had predicted about His Passion: "But a time is coming,
and has come, when you will be scattered, each to his own home. You will leave me all alone." Jesus' apostles' homes were mostly in Galilee, so is that where they would have been scattered to?

We know from John 20 that Thomas, despite being one of "the eleven" whom Luke 24 says were at Jesus' first appearance to the apostles, was not present at that appearance either. In John 21, Thomas is depicted as fishing with Peter in Galilee, albeit over a week later.

In the noncanonical Gospel of Peter, after Jesus' passion and before Jesus makes any appearances to the disciples, Peter does go with a few other Christians to fish in Galilee instead of staying in Jerusalem. However, I am aware that we cannot rely on the "Gospel of Peter".

what and where was Jesus' first appearance to Peter? And where was Peter at that time? Is there any information passed down in our Church tradition about this particular appearance?

In 1 Corinthians 15:5 Paul speaks about Jesus after His resurrection:

"And that He was seen of Cephas, then of the twelve"

I don't understand how that could have been twelve and not eleven. Judas Iscariot, as seems to follow from the Gospels, committed suicide before Jesus was crucified, and, as follows from the book of Acts, Matthias was chosen to be the twelfth one (instead of Judas) already after Jesus' ascension. That means that throughout the whole time from Jesus's resurrection until His ascension, that is, for 40 days (Acts 1:3), there were always only eleven, not twelve. So why does Paul say "twelve" here?

Note there is no mention in the gospels where cephas met Jesus alone?