Most of these church father's writing themselves were likely forgeries... As for John writing John this is problamic in many ways. Ireanuis writing are admitably forgeries of the late second and early third centuries and even if a guy did pen John named John what portion did he pen?
1. The seven signs from John 1-15?
2. The Prayer in 16-18 (An addition)
3. The passion in 19,20 (based on the gospel of Pontius Pilate so early second century)
4. The last chapter likely very late in early third century
5. Lastly the 7:53-8:11 narritive... added after the Vulgate 400+CE