Fractional Jet Pilot reported a NMAC while turning base leg for the final approach when a light twin aircraft cut under their aircraft and causing an RA event. The pilot took evasive action by climbing away from the twin and ATC sequenced them again for landing.

Narrative

Cleared the visual into ZZZ - ATC told us we had traffic 7 o'clock and we verified we were looking for Aircraft Y. Aircraft Y verified they had us in sight and would follow us into ZZZ. ATC directs us to tower and we are cleared to land; #2 behind Aircraft Z short final. As we continued to slow and descend on a right base for Runway XX; a Aircraft Y turns under us and cuts us off causing the RA to climb around 4500 ft. I have been hand flying so I immediately climb as the RA commands and we notify ATC. Once we are clear of conflict 500-900 ft. higher in altitude; they turn Aircraft Y around and we continue on down for the field. After this I asked pilot monitoring (PM) to verify what the sequence is into the field. We are now #1 cleared to land XX and proceed to land without another issue. RA command to climb. ATC needs to be vigilant in keeping airplanes separated and having these pilots punished for flying in an unsafe manner. The line guys at [the FBO] said these Aircraft Y drivers do this frequently and that it seems to be a reoccurring problem.