A PA28 PLT RPTS NARROWLY MISSING AN ACFT TALKING WITH ATC WHILE THE RPTR WAS COMING ONTO THE FREQ.

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CLBING VFR OUT OF 5700 FT TO 7500 FT IN THE PROCESS OF ESTABLISHING CONTACT WITH NEW YORK APCH FOR FLT FOLLOWING; CTLR DID NOT RESPOND TO INITIAL CONTACTS. ON 3RD ATTEMPT CTLR RESPONDED. THEN STARTED GIVING ADVISORIES TO ANOTHER ACFT ABOUT VFR TFC 12 O'CLOCK POS 1.5 MI CLBING OUT OF 6000 FT I NEVER HEARD ANY INFO BEING GIVEN TO MY ACFT USING MY N NUMBER. HOWEVER; CTLR STARTED TO SOUND CONCERNED. I FELT ACFT HE WAS TALKING ABOUT COULD BE ME. I STARTED TO DSND OUT OF 6300 FT BACK TOWARDS 6000 FT. OTHER ACFT CALLED US IN SIGHT. SHORTLY AFTER; I SAW THE ACFT EMERGING FROM BEHIND CTR WINDSHIELD POST. AT THAT POINT NEITHER ACFT WERE CONVERGING VERTICALLY. ALTHOUGH WE HAD TAKEN CORRECTIVE ACTION NEITHER ACFT TOOK AGGRESSIVE EVASIVE ACTION AND CTLR NEVER ISSUED OTHER ACFT AN ADVISORY TO CLB. I AM VERY DILIGENT IN SCANNING FOR TFC; ONE REASON I OWN A LOW WING ACFT. I WILL CONTINUE TO DILIGENTLY SCAN FOR TFC. I COULD HAVE ATTEMPTED CONTACT EARLIER WITH NEW YORK APCH AND I AM LOOKING INTO A PORTABLE ONBOARD TRAFFIC ADVISORY SYS. I THINK THE SYS WORKED ALTHOUGH I WOULD LIKE TO HAVE VISUALLY IDENTED THE TFC SOONER.