MLG FOLLOWED THE WRONG ACFT ON A VISUAL APCH AND HAD A CONFLICT AND A TCASII TA WITH ANOTHER ACFT.

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WE WERE ON A DOWNWIND VECTOR (050 DEG HDG; 4000 FT MSL; 190 KTS) FOR AN LDA A APCH TO LGA'S RWY 22. WX CONDITIONS: 7000 FT BROKEN; VISIBILITY 7 MI; WIND 240 DEGS AT 5 KTS. NEW YORK APCH CTL CALLED 'TFC 11 O'CLOCK; 3000 FT; A FOKKER;' AND ASKED IF WE HAD THE TFC. BOTH THE CAPT AND I SAW TFC AT OUR 10 O'CLOCK POS AND BELOW US ON WHAT LOOKED TO US AS BEING ON FINAL FOR RWY 22 AT LGA. WE ACKNOWLEDGED THE TFC AND WERE GIVEN CLRNC FOR A VISUAL APCH TO CROSS RWY 22 WITH AN ALT RESTR TO CROSS 11 DME (LGA) AT OR ABOVE 3000 FT MSL. OUR POS AT THIS TIME WAS APPROX 10.7 - 10.8 DME FROM LGA. WE TURNED BASE LEG (HDG APPROX 310 DEGS MAGNETIC) AT 4000 FT MSL. ONCE ESTABLISHED ON BASE WE STARTED A DSCNT TOWARD 3000 FT. WHILE IN THE TURN WE WERE TOLD TO CONTACT THE TWR AND I SWITCHED TO LGA TWR. AT 3800 FT MSL WE RECEIVED A TCASII WARNING AND THE DISPLAY SHOWED TFC 800 FT BELOW; DSNDING AT OUR 3 - 3:30 O'CLOCK POS. I LOOKED OUT MY SIDE WINDOW AND SAW THE TFC. I IMMEDIATELY CALLED STOP DSCNT (NO RA ALERT SOUNDED). AT THIS POINT; WE CLBED BACK TO 4000 FT BUT CONTINUED THE TURN TOWARDS FINAL COURSE. WE TRIED SEVERAL ATTEMPTS TO NOTIFY LGA TWR OF THE CONFLICT. ONCE THEY REALIZED THE SIT; HDG AND ALT INSTRUCTIONS WERE GIVEN. WE CIRCLED BACK AROUND FOR ANOTHER VISUAL APCH AND LANDED. HUMAN PERFORMANCE CONSIDERATIONS: OUR PERCEPTION OF TFC GIVEN; THE CTLR'S PERCEPTION OF TFC GIVEN TO US; AND THE CONFUSION OF BOTH PARTIES. ACTIONS WERE IMMEDIATE AND SELF CORRECTING. PREVENTION OF THIS HAPPENING AGAIN WILL COME ABOUT WITH HEIGHTENED SITUATIONAL AWARENESS FROM BOTH PARTIES.