LJ45 FLT CREW EXPERIENCED CONFLICT WITH TFC LNDG RWY 24 DURING PATTERN ENTRY FOR VISUAL APCH RWY 19 AT TEB.

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NEW YORK APCH WAS VECTORING US FOR A VOR DME ALPHA APCH TO TEB ARPT. NEW YOUR APCH CLRED US FOR THE APCH TO TEB; TO GO OVERHEAD THE ARPT FOR A L DOWNWIND RWY 19; AFTER XING CLIFO; DSND TO 1500 FT AND CONTACT TEB TWR. AS WE PASSED OVER CLIFO INTXN; WE CONTACTED TEB TWR; AT WHICH TIME THEY CLRED US TO COME UP OVERHEAD AT 1500 FT TO ENTER A L DOWNWIND FOR RWY 19 AND TO COME BACK TO APCH SPD. MOMENTS LATER; THE TWR ASKED WHERE WE PARKED. I SAID FBO X. AT THAT POINT; THE TWR SAID WE WERE TO FOLLOW A BEECH JET AT OUR 10 O'CLOCK POS; 3 MI. I ACKNOWLEDGED THAT WE WOULD FOLLOW THE BEECH JET; BUT THAT IT WAS NOT IN SIGHT. THE TWR GAVE US A 'ROGER.' WE CAME UP OVERHEAD AT 1500 FT AND STARTED A DOWNWIND FOR RWY 19. I SAW ONE ACFT ON SHORT FINAL FOR RWY 19 AND STARTED A SLOW DSCNT. I WAS ABOUT TO ASK TWR OUR SEQUENCE; WHEN THE TWR CAME ON AND TOLD US TO DO AN IMMEDIATE R TURN AS WE WERE CUTTING ACROSS TFC. AT THIS POINT; I WAS A LITTLE CONFUSED AS TO WHAT HE MEANT. I HADE DSNDED TO 1275 FT WHEN THE TWR CAME BACK WITH 'I HAVE A TFC ALERT; TURN R AND CLB BACK TO 1500 FT;' WHICH I DID. HE ASKED IF I HAD THE BEECH JET IN SIGHT; 11 O'CLOCK POS; 1 MI; BELOW US. I ACKNOWLEDGED THAT I SAW A CITATION X; BUT DIDN'T HAVE THE BEECH JET INSIGHT. TWR INFORMED ME HE WOULD TELL US WHEN TO TURN 'BASE LEG.' I HEARD THE TWR CLR AN ACFT TO LAND ON RWY 24. WITH THAT; I HAD MY COHORT QUESTION TEB TWR AS TO WHICH RWY WE WERE TO USE. THE TWR CAME BACK WITH 'FOR THE THIRD TIME; CLRED TO LAND ON RWY 24.' THAT WAS THE FIRST TIME WE HEARD THE INSTRUCTIONS TO LAND ON RWY 24. THANKS TO THE 'TFC ALERT' IN THE TWR; AN INCIDENT; OR WORSE; AN ACCIDENT; WAS PREVENTED.