Where does “Γενέσιος” come from?

Γενέσιος (Ancient Greek) comes from Ancient Greek -ῐος, from Proto-Indo-European -yós — Creates adjectives from noun or verb stems.

Ancestry of “Γενέσιος”, step by step

Step	Language	Word	Meaning
1	Ancient Greek	-ῐος	belonging to; of”, “belonging to”, “pertaining to
2	Proto-Indo-European	-yós	Creates adjectives from noun or verb stems

Γενέσιος — Etymology, Origin & Word History | Etymology Explorer