All of Augustine and Chrysostom are on Peter being the Rock. You will find no TRUE Church Father talking about Peter’s confession being the rock. That is just a Protestant belief to help them find a way to refute Papal Supremacy.
Another member here posted this on another thread-
(If that poster sees this ,i hope its okay to use your post)
*None of the fathers would claim that the Church is founded on only one apostle. Many had great things to say about the great apostle St Peter. But the rock is the confession of faith.
A friend of mine (a priestmonk) once had this to say:
Let us look at a quick summary of the way that the Church Fathers interpreted that verse -
“Thou are Peter and upon this rock…”
Archbishop Kenrick of Saint Louis, who was one of America’s
extraordinary bishops, was opposed to the doctrine of
papal infallibilty and at the First Vatican Council
in 1869 he voted against it. He wanted to deliver
a speech against the proposed doctrine at the Council
but instead he ceased to attend the Council meetings.
In his speech prepared for, but not delivered in, the
Vatican Council, and published at Naples in 1870,
he declares that Roman Catholics cannot establish
the Petrine privilege from Scripture, because of the
clause in the Creed of Pius IV, binding them to
interpret Scripture only according to the unanimous
consent of the Fathers.
And he adds that there are five different patristic
interpretations of St. Matt. 16:18
Let’s look at how the Church Fathers line up over this verse:
1…“That St. Peter is the Rock” is taught
by seventeen (17) Fathers
2…That the whole Apostolic College is the Rock,
represented by Peter as its chief,
is taught by eight (8) Church Fathers
**3…That St. Peter’s faith is the Rock,
is taught by forty-four (44) Church Fathers **
4…That Christ is the Rock,
is taught by sixteen Fathers (16)
5…That the rock is the whole body of the faithful.
Archbp. Kendrick gives no figure.
Archbishop Kendrick summarises
“If we are bound to follow the greater number
of Fathers in this matter, then we must hold
for certain that the word “Petra” means not Peter
professing the Faith, but the faith professed by Peter.” *