score:2
I found a reference of a shrine, by the sea. It does not say the location, and it was not a church but probably a minor building.
Yet, this shrine could have been build before (in the same place) of the nowadays Rum Orthodox Ayios Fokas Church (saint Phocas Church), which albeit being placed quite north in the Galatha, it is placed right by the sea.
This makes sense, since building a shrine out of the walls was a good option, instead of building an entire church.
Saint John is difficult to pin here, since there are many Saint Johns.