The father in Dostoevsky's The Brothers Karamazov is Fyodor Pavlovich Karamazov.
Fyodor is the selfish, pleasure-seeking patriarch of the Karamazov family and the father of Dmitri, Ivan, and Alexei. He is also rumored to be the biological father of Pavel Smerdyakov, a servant in his household. Fyodor's neglect of his children shapes the family’s emotional and moral conflicts.
His most explosive relationship is with Dmitri, who believes that Fyodor is withholding his inheritance. Their rivalry is intensified by their mutual interest in Grushenka, and the dispute eventually becomes central to the novel's murder plot and courtroom drama. Fyodor's behavior is deliberately grotesque, combining comic vulgarity with real cruelty.
The answer can be confused because Fyodor is also the first name of the novel's author, Fyodor Dostoevsky. The three brothers are Dmitri, Ivan, and Alexei—also called Alyosha—not Fyodor. The patronymic “Fyodorovich” in the brothers' names means “son of Fyodor,” another clue to their father's identity.