FLC OF A CITATION DSNDING FOR A VOR DME APCH HAS NMAC WITH A TWIN ENG ACFT.

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NEW YORK APCH CTL ISSUED A CLRNC; FLY HDG 100 DEGS TO JOIN VOR DME A APCH COURSE FOR TEB ARPT. AS WE BECAME ESTABLISHED APCH CTL BEGAN TO CALL NUMEROUS TARGETS (VFR) IN AREA. CONDITIONS WERE NIGHT; VMC; VISIBILITY APPROX 15 MI. AS THE PNF; I WAS AGGRESSIVELY LOOKING FOR TFC. DUE TO OUR ALT AND GND LIGHTS; IT WAS VERY HARD TO SEE TFC AT ALL. THE ACFT HAD ALL LIGHTS ON (BELOW FL180). AT APPROX 15 NM TEB; THE CLRNC CROSS WANES (TEB 10.8 DME) AT 3000 FT; CLRED VOR DME A WAS ISSUED. AS THE ACFT CROSSED WANES; APCH CTL CALLED TFC AT 10-11 O'CLOCK; ALT MID 2000'S (2500 FT). APCH CTL TOLD THE VFR ACFT 'CITATION WILL BE OUT 3000 FT FOR 2000 FT.' AS THE ACFT APCHED JAYMO (TEB 7.8 DME); APCH CTL TOLD US TO DSND TO 2000 FT IMMEDIATELY. THE VFR ACFT SAID 'I HAVE THE TFC IN SIGHT.' WE WERE NOT IN VISUAL CONTACT WITH THE VFR ACFT. THE ACFT WAS NOW PASSING THROUGH 2300 FT (TEB 5.6 DME) WHEN THE CAPT (PF) PUSHED FORWARD ON THE CTLS. AT THAT INSTANT; I SAW AN ACFT COMING 90 DEGS TO OUR FLT PATH; 100-150 FT ABOVE US (DIRECTLY ABOVE); A BLUR OF LIGHT. AT THAT TIME; I INFORMED NEW YORK APCH CTL THAT WE WISHED TO RPT 'A NEAR MISS.' I DO NOT BELIEVE THAT THE CONFLICTING VFR ACFT EVER HAD US VISUALLY. THE NEW YORK APCH CTLR RESPONDED; 'I HAVE BEEN CALLING TFC (TO YOU); HE HAS YOU IN SIGHT;' THEN GAVE US THE APCH CTL TELEPHONE NUMBER. CAPT CALLED THE PROGRAM MGR ON DUTY. CAPT STATED THAT HE THOUGHT THE CONFLICTING ACFT WAS A SENECA. RECOMMENDATION: TCASII WOULD HAVE IMPROVED OUR AWARENESS OF THE POS OF OTHER ACFT IN A HIGH DENSITY AIRSPACE; AND GIVEN US WARNING OF POSSIBLE CONFLICT(S) AND CONFLICT RESOLUTION.