What is the schwa in linguistics and where can I find it in Ancient Greek?

For what is a schwa, I refer you to What is the schwa in linguistics?, and Schwa – Wikipedia. It is the “neutral”, mid central vowel.

You’ll find the schwa in lots and lots of languages, including English (uh…. ; about; and in fact most unstressed vowels of English). You won’t find it in Ancient Greek.

Schwa used to be reconstructed in Proto-Indo-European though, as the phoneme behind the correspondence of i in Indic to a in Greek. For example, pitár ~ patēr was reconstructed as *pəter-. The distribution of the “schwa indogermanicum” was somewhat problematic, and it is now more economically reconstructed as a syllabic laryngeal (*p-h̥₂ter-); it’s plausible that in late Indo-European, the earlier syllabic laryngeal would have been pronounced as a schwa.