None. Caliphs came to power in the Medieval Period.

As for the Medieval period, the Caliphs were the leaders of the Muslim Empires called Caliphates. The four first Caliphs were called the Rightly-Guided Caliphs and they also had some religious authority in Islam. Because of the barbarity of the Umayyad Caliphs, the religious authority left the Caliphs and vested in the local Imams. Religious authority would return to the Caliphs in the mid-1500s in the Ottoman Empire until Atatürk abolished the Caliphate in 1936.

There was no rule of caliphs in ancient Rome. The caliphs emerged after the fall of Rome

Ali was the last of the Orthodox caliphs.

Hazrat Ali RAU was the Fourth and last Rashidoon Caliphs.

Yes. The Caliphs are the political successors to Muhammad.