The Exiled by Christopher Charles ticks all the boxes for a solid mystery - baffling murder, troubled hero with a complicated past, perceptive sidekick, and a love interest. Wes Raney is living in self-imposed exile in New Mexico when he's called in to investigate a triple murder. The action moves back and forth in time between the present-day investigation and the catastrophic events in New York City that lead to Wes's downfall in the 1980's.
The Exiled has some similarities to another muscular mystery set in New Mexico, American Blood by Ben Sanders. The hero of American Blood, Marshall Grade, is living in witness protection after a failed undercover operation in his past life as a police officer in New York City. He is drawn into a search for a missing woman. He puts his cover story, and his life, in jeopardy.