The Father is the unnamed antagonist of the famous Aerosmith song "Janie's Got a Gun" - which tells via lyrics the tragic tale of a girl who gains vengeance on her abusive father via a fatal shooting sparked by a sexual assault committed by said father, which drove her to extreme measures.
Although never mentioned directly, the song refers to the Father in lines such as "what did her daddy do?" - the music video shows the crime in more detail, though, as is normal in music-based stories, much of the plot is left to the viewer's own imagination.
The line "He jacked a little bitty baby" was originally "He raped a little bitty baby" but was changed, presumably because of the line being a little too controversial even for the song in question. However in live performances the band sometimes use the original line, uncensored.