FLC OF AN ATX LTT OVERSHOT CLB INTERMEDIATE ALT RESULTING IN A TCASII ALERT FROM ANOTHER ACFT ABOVE.

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LEAR JET 35; AFTER DEPARTING OAK; WE WERE GIVEN CLB CLRNC TO 10000 FT. THE COPLT WAS FLYING; I WAS OPERATING THE RADIOS. OPERATING AT A NORMAL CLB OF 4000-5000 FPM IN A LEAR JET 35. BAY DEP POINTED OUT XING TFC AS WE WERE PASSING 8000 FT. THE TFC; XING R TO L AT 11000 FT; WAS AT 11 O'CLOCK AND NO FACTOR. ADDITIONAL TFC WAS CALLED AT OUR 1-2 O'CLOCK POS; ALSO AT 11000 FT. THIS WAS A 757. I WAS SCANNING FOR THE TFC WHILE THE COPLT LEVELED AT 10000 FT. WE LEVELED; AND THE AFTER TKOF CHKS WERE PERFORMED. AT APPROX XA10 LCL (WITHIN 3-5 MINS OF LEVELING); BAY DEP ASKED OUR ALT. I LOOKED AND SAW 10100 FT ON THE CAPT'S ALTIMETER. I RPTED BEING LEVEL AT 10000 FT. NO FURTHER MENTION WAS MADE BY BAY. FURTHER ENRTE ZOA ASKED US TO CALL THE BAY APCH SUPVR WHEN WE REACHED BUR. CALLING AT ABOUT XA15 LCL THE SUPVR ADVISED ME THE PLT DECLARED OUR ACFT OFF ALT AND HE HAD A TCASII ALERT. THE SUPVR FURTHER STATED THE RADAR SHOWED US AT 10300 FT WITH A HIGH RATE OF CLB. I INFORMED HIM I WAS THE PNF AND I SAW OUR ALT AT 10100 FT AND THAT OUR ALT ALERT; WHICH SOUNDS AT 300 FT OFF ALT; NEVER ACTIVATED. HE ASKED ME TO CALL BACK AFTER HE HEARD FROM THE PLT. ON OUR RETURN FLT TO OAK THE ALT ALERTER ACTED IN THE PROPER MANNER; SHOWING THAT WE COULD NOT HAVE BEEN 300 FT HIGH. CALLING THE BAY SUPVR FROM OAK (ABOUT XA30 LCL); I TALKED TO A DIFFERENT SUPVR. HE JUST HAD THE RPT FROM THE OTHER SUPVR; AND THE PLT HAD NOT CALLED. HE STATED THE RPT SAYS THE 757 HAD A TCASII ALERT AND HAD TO DEVIATE. HE RESTATED THE RADAR SHOWED US AT 10300 FT. WE CHKED OUR MODE C WITH VARIOUS CTRS AND FOUND NO DISCREPANCIES.