I first became aware of anaptyctic vowels when reading about Mehri. Mehri is spoken in southern Arabia and the islands of the south. It branches off the Semitic language family. Regarding epenthesis, anaptyxis specifically, "anaptyctic vowels are common" in Mehri (Bergsträsser 152).
Epenthesis of a vowel, anaptyxis, means "growth" in Greek. Anaptyxis specifically within a word manifests historical sound changes from earlier forms of a word to later forms. Take for example bradar to the Persian baradar (brother). Another example is the Latin stabilis from *stablis (Johnson 95).
Anaptyxis is hard to identify in Old Persian: "But in Ancient Persian u between d and r, and between g and d, when the following syllable or the preceding syllable has an u-sound, furnishes the only sure examples of anaptyxis" (Johnson 95).
It is more easily identified in Avestan. The examples Johnson identifies are GAv. dadǝmahī (we give) – Skt. dadmasi; GAv. fǝrā (forth) – YAv. frā, Skt. prā. Professor Skjærvø (Harvard) identifies some other great examples of anaptyxis in Avestan: patarō / *ptarō (fathers); zarazdāiti- / zrazdāiti (faith), Skt. śraddhā-. Skjærvø says in Avestan anaptyxis is found occasionally between stops, between z and r, between s and following consonant in word and sentence sandhi, between two spirants followed by r, between v or uu and ii, between y or ii and uu, and between consonant and ii.
Bergsträsser, Gotthelf. Introduction to the Semitic Languages: Text Specimens and Grammatical Sketches. trans. Peter T. Daniels. Eisenbrauns, 1983.
(Bergsträsser, Gotthelf. Einführung in die semitischen Sprachen. 1928.)
Johnson, Edwin Lee. Historical grammar of the ancient Persian language. 1917.
Skjærvø, Prods Oktor. "An Introduction to Young Avestan: rechecked 4th version." 2003. (PDF, Harvard)