NMAC BTWN ACR X AND UNKNOWN Y.

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AT XX02Z; I TOOK THE S ARR POS COMBINED WITH W AND 1/2 OF FV POS. THE PREVIOUS CTLR BRIEFED ME THAT AN ACFT OVER RWY 17N WAS CLBING TO 13500 FT WITH JUMPERS AND NEEDED TO BE POINTED OUT TO ZDC AND ZNY. I MADE THE POINT OUT TO ZDC BUT ZNY DIDN'T ANSWER. THEN ACR X; WHO WAS ON VECTORS FOR A VISUAL; ASKED TO BE VECTORED OUT FOR THE ILS TO GET TIME FOR THEM TO FINISH IN THE BACK. I SAID NO PROB AND TRIED THE POINT OUT AGAIN. NO ANSWER AGAIN. THE S DEP POS 'APPROVAL REQUESTED' A SLOW CLB TO DITCH; WHICH I APPROVED AND HAD TO WATCH TFC FOR IT; A VFR OVERFLT WHICH WAS PASSING OVER RWY 17N AS THE JUMP ACFT CLBED INTO ZNY SPACE. I TRIED THE POINT OUT AGAIN AND AS I DID; I SAW UNKNOWN TFC; UNKNOWN Y AT 2600 FT IN FRONT OF ACR X. I XMITTED 'ACR X HVY; TFC ALERT; 12 O'CLOCK; 1 MI; SBOUND; 2600 FT UNVERIFIED.' HE SAID 'WE DON'T SEE HIM; BUT WE HAVE A RESOLUTION AND WE'RE FOLLOWING IT.' I SAID 'ROGER.' AS HE PASSED OVER THE TARGET ACR X RPTED THE ACFT IN SIGHT. I SAID ROGER AND TURNED HIM ONTO FINAL. HE RPTED THE ARPT IN SIGHT AND I CLRED HIM FOR A VISUAL APCH. HE THEN SAID 'THAT WAS A NEAR MISS AND I'LL HAVE TO FILE A RPT.' I SAID ROGER AND ADVISED THE SUPVR. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: ASKED RPTR IF THE UNKNOWN ACFT HAD BEEN OBSERVED IN THE CLASS 'B'; AND WAS TOLD THAT HE WAS UNSURE BUT THAT THE ACFT APPEARED TO BE ON THE EDGE OF IT. WHEN ASKED IF THE B767 HAD TAKEN EVASIVE ACTION; THE RPTR INDICATED THAT THEY HAD THE TFC IN SIGHT AND LEVELED OFF UNTIL CLR OF THE TFC.