Medium Transport; Low Wing; 2 Turbojet Eng
Flight Crew Air Transport Pilot (ATP)
Situational Awareness; Confusion; Workload
Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Clearance; Deviation / Discrepancy - Procedural Published Material / Policy; Inflight Event / Encounter CFTT / CFIT
Air Traffic Control Issued Advisory / Alert; Flight Crew Became Reoriented; Flight Crew Requested ATC Assistance / Clarification
Procedure; Weather
We were flying the VOR 4 approach to LGA. We followed all the step downs on the approach down to 600 feet. Shortly before we broke out; Tower told us that we were right of course and they had a low altitude alert on us. Tower gave us the altimeter setting and I confirmed that we had set the correct altimeter setting.  While I was confirming the altimeter setting with Tower; I saw the runway which was slightly to the left. I told Tower that we had the runway and we landed.I'm not sure why Tower got a low altitude alert and as for being slightly to the right of course; it was a non- precision approach.
LGA Tower issued a low altitude alert to an air carrier on the VOR 4 approach because the flight was right of course. The crew; level at 600 feet; was puzzled by the alert and shortly there after had the runway in sight slightly left.