Which preposition to use with tetrarchy

in Occurrences 1%

The people of Amisus he rewarded with freedom, and to Mithridates the Pergamenian he gave a tetrarchy in Galatia with the name of kingdom and allowed him to wage war against Asander, so that by conquering him, because he had proved base toward his friend Mithridates might get Bosporus also.

of Occurrences 1%

To Herod he entrusted the tetrarchy of a certain Zenodorus and to one Mithridates, though a mere lad, Commagene, since the king of it had killed his father.

Which preposition to use with  tetrarchy