Church History VI.14.7 (Clement on John) — Nicene and Post-Nicene Fathers, series 2, vol. 1 (Arthur Cushman McGiffert, 1890) (public domain)
5. Again, in the same books, Clement gives the tradition of the earliest presbyters, as to the order of the Gospels, in the following manner:
The Gospels containing the genealogies, he says, were written first. The Gospel according to Mark had this occasion. As Peter had preached the Word publicly at Rome, and declared the Gospel by the Spirit, many who were present requested that Mark, who had followed him for a long time and remembered his sayings, should write them out. And having composed the Gospel he gave it to those who had requested it.
When Peter learned of this, he neither directly forbade nor encouraged it. But, last of all, John, perceiving that the external facts had been made plain in the Gospel, being urged by his friends, and inspired by the Spirit, composed a spiritual Gospel. This is the account of Clement.
Reproduced in full. Translation: Nicene and Post-Nicene Fathers, series 2, vol. 1 (Arthur Cushman McGiffert, 1890) (Public domain).
Why Pitre cites it
Clement of Alexandria's remark, preserved by Eusebius, that John 'composed a spiritual Gospel' — Pitre's warrant for reading a second level in Jesus' words from the cross.
Notes
§§5–7 (§7 has the key phrase; §§5–6 supply the Clement context on the order of the Gospels).