A former Rikers Island correction officer has been convicted in the cold-case shooting death of his ex-girlfriend 13 years ago.

Christopher Clavell faces 25 years to life in prison when he is sentenced for firing nine shots at Barbara Perez behind a gym in Ridgewood, Queens, where she was employed as a manager.

Prosecutors argued that Clavell was driven to kill Perez in 2000 because of “child-support obligations” and he repeatedly harassed and confronted her about it.

Perez told family members that Clavell stated that he would sooner kill her than give her money, Queens DA Richard Brown said after Thursday’s conviction.

Clavell, 48, was denied custody and Perez’s parents were awarded baby Brian and his older brother, Michael. The 20-year veteran correction cop wasn’t arrested for the crime until April 2011, but he was questioned at the time of the shooting.