N90 TRACON APCH CTLR INCORRECTLY IDENTS TFC A BA41 IS TO FOLLOW. AS THE BA41 TURNS TO FOLLOW TFC; APCH CTLR ADVISES THAT HE ISSUED THE WRONG TFC; REQUIRING THE BA41 TO MAKE AN EVASIVE MANEUVER TO FOLLOW INTENDED TFC.

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WE WERE ON A 10 MI R BASE FOR RWY 4R AT JFK. IT WAS MY LEG. APCH CTL GAVE US A TFC CALL 'LEARJET AT 1-2 O'CLOCK. WE CALLED HIM IN SIGHT AND WERE CLRED FOR THE VISUAL APCH RWY 4R FOLLOWING THE LEARJET. THE ACFT MY FO AND I WERE LOOKING AT WAS AT 1-2 O'CLOCK AND ABOUT 5-6 MI SO I TURNED R TO A DOGLEG (HDG ABOUT 310 DEGS). JUST PRIOR TO REACHING THE FINAL APCH COURSE; APCH CTL ASKED IF WE HAD THE LEARJET IN SIGHT. WE REPLIED WE DID. APCH CTL THEN INFORMED US THE LEAR WAS AT OUR 10 O'CLOCK POS AND 2 OR 3 MI AND WE WERE CUTTING HIM OFF. THE TCASI WAS NOW SHOWING THAT TARGET (WE HAD REALLY NOT LOOKED AT TCASI UP TO THAT POINT THINKING WE HAD THE LEAR IN SIGHT WELL IN FRONT OF US) 200 FT HIGH AT 10 O'CLOCK. WE TURNED L TO GET BEHIND THE LEAR AND CONTINUED OUR DSCNT TO STAY BELOW HIM. WE NEVER SAW THE LEARJET BUT ESTIMATE WE CAME WITHIN 1-2 MI AND 300 FT VERTLY FROM HIM. ONCE WE WERE WELL CLR OF THE LEAR; APCH CTL ALLOWED US TO TURN BACK TOWARD THE RWY TO CONTINUE THE APCH AND REMARKED; 'SORRY ABOUT THAT; I MAY HAVE GIVEN YOU THE WRONG CLOCK POS.' NO FURTHER ACTION WAS TAKEN AND WE LANDED UNEVENTFULLY. A NOTE ON THE TCAS: OUR SYS IS TCASI AND WE NEVER RECEIVED A TA.