Fabian has a very minor role in Shakespeare's Twelth Night, appearing only in Act II, Scene V; Act III, Scene IV; and Act V, Scene I. He is essentially one of Shakespeare's stock characters, a character type that appears over and over again in Shakespeare's works. In particular, he can be classified as the stock character identified as a servant and partially as the stock character identified as a "clever servant" (Schwartz, "Shakespeare's Plays: Comedy").
In Act II, Scene V, we learn that Fabian has fallen "out o' favour with" Olivia because Malvolio tattled on him. Wanting revenge, Fabian joins in on Maria's and Sir Toby's plot to humiliate Malvolio by making him believe Olivia is in love with him. It is in joining the plot that Fabian demonstrates he is a clever servant. Plus, as both a prankster and a clever servant, he gets involved in the duel between Andrew and Cesario in Act III, Scene IV.