DURING AN LDA-A APCH TO RWY 22 AT LGA; THE FLC OF AN FK10 TOOK EVASIVE ACTION TO AVOID ANOTHER ACFT THAT HAD INADVERTENTLY FLOWN INTO THE FINAL APCH PATH. ANOTHER CTLR WAS TALKING TO THE SMA ACFT AND HAD ATTEMPTED TO TURN THE ACFT AWAY FROM THE LGA APCH COURSE; BUT WAS INEFFECTIVE AND ALSO UNABLE TO INFORM THE CTLR FOR THAT SECTOR.

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ON BASE LEG LGA LDA-A RWY 22 AND CLRED FOR VISUAL TO FOLLOW COMPANY B737 WHICH WE HAD JUST CALLED IN SIGHT. FO WAS PF AND BEGAN DSCNT. JUST ABOUT AS WE ROLLED OUT ON OUR ASSIGNED HDG; TO TURN TOWARDS THE ARPT; GOT A TA THEN IMMEDIATELY AN RA; WITH A VOICE SAYING TO CLB. I HAD LOOKED AT TCASII IN NORMAL SCAN AS WE WERE ROLLING OUT OF TURN TO ASSIGNED HDG PREPARING TO READ LNDG CHKLIST WHEN WE GOT TA AND THEN THE RA TO CLB. I SAID TO THE FO; 'CLB AND BREAK R AS A BACKUP;' AS HE WAS ALREADY ADDING FIREWALL PWR. AS HE CLBED AND STARTED TURNING R; I SAW A SINGLE ENG; LOW WING ACFT; POSSIBLY A BEECH; PASS UNDER US. I ADVISED APCH OF OUR EVASIVE MANEUVER; FINISHED THE CHKLIST; AND INFORMED THE PAX AND FLT ATTENDANTS THAT ALL WAS WELL. REMAINDER OF THE FLT WAS UNEVENTFUL. I SPOKE TO THE ATC SUPVR BY LANDLINE AND WAS TOLD THAT THE SINGLE ENG ACFT STRAYED OVER TO OUR AREA AND WAS BEING TOLD BY ANOTHER CTLR TO TURN AWAY FROM LGA APCH COURSE. THE OTHER CTLR DID NOT HAVE TIME TO INFORM OUR CTLR TO TELL US OF THE TFC.