You need to contact the Court. It may be that given your delay, you have been defaulted on NY summonses. The Court will be able to inform you of status.
In NJ if you fail to pay the ticket you have to appear on the date set on the ticket. If you do not appear one of two things happens. The court orders a second notice demanding your appearance or it files an FTA and sometimes puts a warrant out. The FTA will go to Trenton and they will notify NY and NY will suspend your license under the interstate compact. You have to call the Court. Find out what happened. Post the bail or just go down and pay the ticket. If Court appearance is ordered it is because they are going to hit you for a contempt for failing to pay or show. My advice is to clear this up ASAP or your license is at stake.
In addition to suspending your license, a Municipal Judge has the power to issue a warrant for your arrest and they do so often. At some point, a police officer will scan your plates and you will be pulled over and taken to the town police station and held there until you post bail. If you cannot post bail, you will be taken to the county jail. Maybe you get pulled over in one of the more affluent towns and will be the only person in the booking area. Maybe you get pulled over in Irvington or Newark or Camden and have a different experience. Call the court where the ticket was issued immediately and find out what the status of your ticket is and what you have to do to take care of it.