His surname was Doria, but since he belonged to the ruling house of Arborea he is often dynastically called Bas-Serra, or Doria-Bas.
He was born at Castel Genovese (modern Castelsardo) in 1377 to Eleanor and Brancaleone Doria, a Genoese nobleman.
Upon Hugh's death in a republican uprising, the barons of the realm gathered in a parliament and elected Frederick judge.
No sooner, the Giudicato fell into another bitter war with the Crown of Aragon, who laid claim to the island.
During the war, Frederick was captured together with his father by its monarch Peter IV of Aragon, and they both were imprisoned in Cagliari, first in the tower of San Pancrazio and then in that of Elefante.