Complex sentence: They may have been descended from the Chaghān Khudās who ruled Chaghaniyan during the early Middle Ages; another possibility is that their ancestors were Arabs who migrated to the region and were Iranicized.
Split into simpler sentences: They may have been descended from the Chaghan-kodas who ruled Chaghaniyan during the early Middle Ages. Another possibility is that their ancestors were Arabs who migrated to the region and were Iranicized.