Hi Gandalf, I am assuming that you are debating the Matthew 16 rock text.
Fitzmyer, purposed the aramaic kepha kepha reading in a few books,
Joseph A. Fitzmyer, “Aramaic Kepha’ and Peter’s name in the New Testament,” Text and Interpretation: Studies in the New Testament presented to Matthew Black, ed. Ernest Best and R. McL. Wilson
To Advance the Gospel: New Testament Studies (The Biblical Resource Series) by Joseph A. Fitzmyer
But later in Queries & Comments," Biblical Archaeology Review 19.3 [1993], 70 fitzmyer refutes the kepha kepha reading based on the fact that it does not account for the greek play on words.
Personally, I think Jesus likely taught in Hebrew,
The question of authenticity assumes an altogether special aspect in regard to the First Gospel. The early Christian writers assert that St. Matthew wrote a Gospel in Hebrew; this Hebrew Gospel has, however, entirely disappeared, and the Gospel which we have, and from which ecclesiastical writers borrow quotations as coming from the Gospel of Matthew, is in Greek.
newadvent.org/cathen/10057a.htm
Read this article to find which fathers wrote on the language question of Matthew, but as you check each reference in the fathers themselves, the case is up in the air if Matthew wrote in Hebrew, Aramaic or whatever.
newadvent.org/cathen/10057a.htm
Your best case from your perspective, would be to go the Fathers themselves to see how they interpreted Matthew 16 rock passage.
Some of the Fathers, saw the rock as Christ, others as Peter, and so on.
For example the The Shepherd of Hermas (Book III, Similitude 9) CHAPTER XII makes the rock that the church is built on Jesus as the Son of God,
“First of all, sir,” I said, “explain this to me: What is the meaning of the rock and the gate?” “This rock,” he answered, “and this gate are the Son of God.”
newadvent.org/fathers/0201309.htm
On second thought you are better off asking them to explain
Ephesians 2:20 (King James Version)
And are built upon the foundation of the apostles and prophets, Jesus Christ himself being the chief corner stone;