What happens when you cast Michael Sheen as a brilliant psychopath and serial killer then don’t use him for more than eight or nine minutes per episode? We spend the other 30 minutes wondering why he isn’t onscreen.

“Prodigal Son,” Mondays on Fox, is yet another variation on “Silence of the Lambs,” with Sheen as the imprisoned Hannibal Lecter character — here a cardiothoracic surgeon named Martin Whitly — and Tom Payne as his Clarice, a young criminal profiler named Malcolm Bright, who works with him to solve crimes. The twist is that Martin and Malcolm are father and son, and dad’s dark deeds give Malcolm nightmares so vivid that he has to shackle himself to his bed. (We see them in the form of frequent and irritatingly indecipherable flashbacks).

Lecter stories are set up as contests, in both plot and performance, and this is one that Payne can’t win, despite his charm. (He was formerly Jesus, the most likable character on “The Walking Dead.”) Sheen is just too much fun to watch, playing the killer as an exuberant, overgrown child, unable to contain his glee whenever his son arrives for a consultation. Through three episodes, Sheen goes very light on psychotic menace, a refreshing choice that also allows for future revelations about Martin’s motives.

When the show leaves Martin’s cell, it becomes an unexceptional procedural, with Malcolm as the oddball consultant to a team of New York detectives led by his surrogate father figure (played by Lou Diamond Phillips). It’s on the grisly end of the spectrum — victims’ mouths sewn shut, that kind of thing — with studiously eccentric details like Malcolm’s self-shackling, and the Persian carpet and bookshelves in Martin’s apartment-size cell. The murder cases are cursory and dull (too much time goes to the family psychodrama) but things perk up whenever Keiko Agena is onscreen as the medical examiner, whose barely repressed lust for Malcolm renders her incoherent. Like Sheen, she wants us to have some fun.