The off-duty NYPD sergeant who shot a personal trainer inside his home had been arguing with the man — who was home alone with the cop’s wife moments before, according to police and sources.

The 34-year-old sergeant, identified by sources as Justin Ellis, was placed on modified duty after the encounter early Friday at his Nassau County home in Seaford, according to police.

Ellis allegedly came home just after midnight to find the 29-year-old personal trainer inside, according to police and sources.

“He told the guy to get out of his house,” a police source told The Post. “They had some words. The guy went to his car and got a bat. And he shot him.”

The trainer, whose name was not released, was shot in the chest but was expected to be OK.

Ellis, who works in the 103rd Precinct in Queens, told cops the man came at him with the bat, police said.

No charges have been filed in the incident.