John of Alexandria is named as an ἱατρός and commentator in Alexandria in the sixth and seventh centuries CE, among the ἰατροσοφισταί who lectured on earlier Greek medical books.
This site lists no work under his name.
Later copies attach to him a fragmentary Greek commentary on the Hippocratic Epidemics, covering books 2, 4, 5, 6, and 7. That commentary quotes Hippocratic Greek. The Hippocratic books remain those earlier books.
What this page holds is the name, not the commentary.
Available Works
Commentaries-Hippocrates' Book-the Nature of the Child
Ὑπομνήματα εἰς τὸ Βιβλίον περὶ Φύσεως Παίδων
31 passages
Also published as PDF.