where in talmud or halacha can one find about the separation of calling jews ashkenazi or sephardi?

where can one find the talmud text or halachah text or something similar that identifies or divides Jews as either Ashkenazim or Sephardim or Teymanim? (Also, is it two only, the first two only, because the last one, Yemenites or Teymanim, is sometimes left out)?