@sudoyum you will owe VA taxes as a non-resident, since you work there. Then you will owe NJ taxes as a resident.
However, NJ will give you a credit up to the NJ tax rate for the taxes paid to VA, so that you are not taxed twice on the same dollar.
When doing your tax return next year, critical to make sure the VA return is completed BEFORE completing the NJ return. That will make sure the credit appears correctly on the NJ return,