[schoen]

I think you're thinking of the Athenian democracy, because Greece wasn't politically unified at that time.

https://en.wikipedia.org/wiki/Athenian_democracy

I doubt that the Athenians had the present-day concept of "white people". Wikipedia says that citizens "had to be descended from citizens", so maybe at least in a certain era nobody known to be descended from people coming from outside of Athens could be a citizen.

https://en.wikipedia.org/wiki/Athenian_democracy#Citizenship...

Edit: looking at one of the references, it seems that there was a year when explicit citizenship lists were drawn up based on all free men who lived in Athens (maybe with some kind of ethnic exclusion at that time too?). From then on until Pericles, children could be added to the list if their fathers were on the list. After Pericles, children could be added to the list if their mothers and fathers were on the list.