The wanted man has been identified as 26-year-old Sadan Mullings of Elgin Town in Hanover.
Mullings is also wanted in connection with several serious crimes and killings in Westmoreland and St Ann.
One of these crimes police believe is to be the quadruple murder committed in Bath, Westmoreland on Saturday night, March 18.
The police are urging Mullings to report to the nearest police station.
In the meantime, the police have identified an alleged gunman that was killed in Thursday night’s shootout.