Father was the proper form of address for a priest of the Catholic denomination of Christianity on Earth. The character of Mulligan within the Fair Haven holographic program, played by The Doctor, was addressed this way. (VOY: "Fair Haven", "Spirit Folk")
Father is also the title of a male who has parented a child. Alexander often called Worf "father" (TNG: "Reunion", et al.) as did Jake Sisko do with Commander Benjamin Sisko. (DS9: "Emissary", "Move Along Home", et al.)
When Jake Sisko told Varis Sul about his father, Nog tried to compare his father, Rom, to Jake's. Both were more silent when Varis Sul told them that her parents were killed by the Cardassians. (DS9: "The Storyteller")