father (n.)
Old English fæder "father, male ancestor," from Proto-Germanic *fader (cognates: Old Saxon fadar, Old Frisian feder, Dutch vader, Old Norse faðir, Old High German fater, German vater), from PIE *pəter (cognates: Sanskrit pitar-, Greek pater, Latin pater, Old Persian pita, Old Irish athir "father"), presumably from baby-speak sound like pa.

The classic example of Grimm's Law, where PIE "p-" becomes Germanic "f-." Spelling with -th- (15c.) reflects widespread phonetic shift in Middle English that turned -der to -ther in many words; spelling caught up to pronunciation in 1500s (compare burden, murder, mother, weather).
father (v.)
c.1400, from father (n.). Related: Fathered; fathering.