New York and New Jersey are both members of the Drivers License Compact (DLC) which means that the states courts and DMV's share information regarding moving violation that their licensed drivers receive out of state. So the NY courts will inform the New Jersey Motor Vehicle Commission (MVC) of your moving violation conviction for failing to stop at a stop sign.
In New York it 3 points for failure to obey a traffic signal, a stop sign or a yield sign. In New Jersey the failure to observe stop or yield signs offense is worth 2 points and that is what you will receive because NJ MVC has decided to assign only 2 points to any out of state moving violations they are notified of.
The MVC will thus assess you points as well as place the New York violation conviction on your NJ driving record. Since the NY offense will be on your driver's history, your insurance company will be able to see it next time they run your motor vehicle record (MVR). Then it could cause your premiums to rise, depending upon your insurance company's rating system.
To find out about your insurance company's rating system either contact your insurance agent or the NJ Department of Insurance with whom insurance companies must file their rates. If your insurance premiums rise due to this traffic violation you can get an NJ online auto insurance quote here with us.