well, the askhenazi (jiddish speaking) might be connected to the khazars, but not the sephardim which still exist (afaik they are treated as 2nd class citizens in israel, because of their darker skin complexion). the sephardim were also everywhere esp in the iberian peninsula and the spanish inquisition scattered them even more including the americas, and the ottoman empire where they joined the islamized sabattean jews.

additionally, the middle eastern jews who choose to stay in iraq even after their babylonian captivity ended until (iirc) 500 ad..

and there are other jews of the orient. families like the sassoons who were in india(?).

i also saw wikipedia articles saying that an alternative name for the scythians was askhenazim. the scythian geographical territory more or less matches overlaps w/ the khazarian empire. they say the scythians loved to use gold in their arts :-)

and i think there are more jews iirc mizraims, ethiopians and possibly others. idk too much about those.