Which Pope had a son who would also become Pope?

Pope Hormisdas was born in Frosinone, Italy. Before becoming a Roman deacon, Hormisdas was married. He had a son. His son would become Pope under the name of Silverius. Pope Silverius died in December 537. He ruled the Holy See from June 536 to his deposition in 537, a few months before his death.

Silverius was a legitimate son of Pope Hormisdas. He was born before his father entered the priesthood. Silverius was a subdeacon when King Theodahad of the Ostrogoths forced Silverius to participate in an election to become pope. Consequently, Silverius received consecration as pope in 536. In the end, Pope Silverius was recognized as a saint by popular acclamation.

Now, he is the patron saint of the island of Ponza, Italy. His name was on a list of saints and first mentioned in the 11th century.