Who was Esther's father?

Answer: Abihail

Esther was the daughter of Abihail, Mordecai's uncle. Jair, Shimei and Kish are named as Mordecai's ancestors.

“Now Esther was the daughter of Abihail, the uncle from whom Mordecai had adopted her as his own daughter. And when it was her turn to go to the king, she did not ask for anything except what Hegai, the king’s trusted official in charge of the harem, had advised. And Esther found favor in the eyes of everyone who saw her.”— Esther 2:15 (BSB)