There are 3 STARs (Standard Terminal Arrival Routes) into JFK that cross over Long Island:
PARCH 3 RNAV ARR:
PAWLING 2 ARR:
ROBER 2 ARR:
None of these have particularly pronounced zigzag patterns, so what you describe is probably not coming from the waypoints of the arrival procedure.
Looking at flightradar24.com, we can currently see ...