A Latin Kings gangbanger suspected in the road-rage killing of an off-duty FDNY firefighter in Brooklyn was arrested Tuesday in New Jersey, authorities and police sources said.

Cops and US marshals tracked Joseph Desmond and a girlfriend to the Circle Motor Lodge in South Amboy, NJ, early Tuesday, and arrested him on a parole violation, according to sources.

Desmond, 29 — a purported Latin King with convictions for assault and drug possession — was not immediately charged with the slaying of firefighter Faizal Coto, but police sources said he’s the prime suspect.

Coto, 33, was driving on the Belt Parkway early Sunday morning when he got into a dispute with the driver of a silver four-door Infiniti registered to Desmond.

When the motorists pulled over near Exit 4 to hash out their issue, the Infiniti driver cracked Coto over the head with a blunt object — which investigators believe to be a baseball bat — and sped off, leaving the firefighter for dead, cops said.

Desmond’s Infiniti wasn’t at the motor inn on Tuesday and investigators are still searching for it, sources said.

As authorities hunt for the car, they’re quizzing both Desmond — a Staten Island resident just released on parole in April — and his girlfriend.

A hearing to extradite Desmond back to New York will be held later this week or early next, New Jersey court officials said.

By that point, Coto, a three-year FDNY veteran who was assigned to Engine 245/Ladder 161 in south Brooklyn, will have been laid to rest.

Coto’s wake is scheduled for Wednesday at Brooklyn’s Leone Funeral Home on Fourth Avenue. His funeral will be at 11 a.m. Thursday.

In an odd coincidence, Coto’s FDNY counterparts battled a blaze Tuesday in his former apartment building in Brooklyn.

About 60 firefighters quashed the fire on the second floor of the building on Ocean Avenue near Church Avenue around 3 p.m., officials said.

No injuries were reported.

When he wasn’t fighting flames with his fellow bravest, Coto was an aspiring rapper who performed under the name FAIYA, according to social-media posts in which he mused on his art and life.

“Anyone that deals with depression, anxiety, insecurity (which is ALL of us at one time or another) pick up an instrument, a sketch pad, a paintbrush, a pair of dancing shoes, a camera . . . something that can capture what you wish to say without words,” he wrote on Facebook, adding in another message, “[T]here’s a bigger picture when it comes to my Life, my Music and the Legacy that I hope to leave behind.”

Additional reporting by Yaron Steinbuch and Stephanie Pagones