Underfell was foremost created as a design aesthetic, so there isn’t a canon back story to the characters outside of the idea that they are an alternative, evil version of the regular Undertale canon characters. Some of the various and widely accepted ideas about the characters, however, are things such as UF Sans getting easily flustered and irritated by flirting, puns, and having an obsession with mustard, or UF Papyrus being a cold individual with no patience for failure (especially not from his brother).

Source: Underfell AUs