Dear All,
Generally speaking, it was a wide-brimmed pointy hat that Jews had to wear. I'm pretty sure the yellow star came a lot later.
However as to golems, golems should be only available to Jews (and really only Ashkenazim - Northern European Jews) in a "historical" setting (unless there are other cultures that I don't know about).
I seem to recall that there are only two references in the Talmud to golems, a calf and a man - although not being Jewish, and thus not a Talmudic scholar, I might have missed others.
The main thing is that Medieval Jewish golems in a game setting should be nothing like D&D golems. They can be eaten (like the calf), act as labour, or most rarely as strictly non-violent guardians (although they can do incidental subdual damage) of the wider Jewish community. The creators (and it seems to have always been a creation of several scholars) can't give a golem free will - it has emotion, but is utterly limited to carrying out its function.
Of course, in a fantasy setting, you can have them doing whatever you want as a GM.
Hope that is of interest.
All the best