Flight Crew Multiengine; Flight Crew Instrument; Flight Crew Air Transport Pilot (ATP)
Other / Unknown
Deviation - Altitude Overshoot; Deviation / Discrepancy - Procedural Clearance
Air Traffic Control Issued Advisory / Alert; Flight Crew Became Reoriented
Procedure
Initial climb out HPN RWY 16 HPN7 departure. Passing through 2000ft climbing 3000ft on the SID profile ATC query's our altitude. We reply and are informed we should have leveled off at 2000ft. We immediately leveled and descended back to 2000ft. Reaching 2000ft we were handed off to the next controller and given a climb.Charted top altitude 3000ft. 2000ft given in verbal ATC departure clearance prior to pushback. Altitude selector initially set off charted top altitude and clearance change in altitude was not caught in brief. Check altitude pre-selector with both clearance altitude and the SID not just the SID.
First Officer reported climbing to the charted SID altitude instead of the initial altitude restriction assigned in their verbal clearance.