You didn't answer my question about whether you worked in NC at all in 2022. I will assume that you did not. If that assumption is wrong, and you actually did work in NC, even for a short time, then much of the following needs to be modified.
Since you are a full-year resident of New Jersey, all of your income is subject to NJ tax, no matter where the income is from. Any income that you earn for working in another state is also subject to tax by the state that you worked in. If you worked only in NJ, none of your income is subject to tax by NC or any other state. The fact that your employer is located in NC does not make you subject to NC tax if you did not actually work in NC.
Note that the tax withheld from your pay is not the final amount of tax that you pay. Your final tax is calculated on your tax return after the end of the year. The withholding is an advance payment towards your actual total tax for the year. If the withholding is more than your actual tax, you get a refund of the excess when you file your tax return. If the withholding is less than your actual tax, you have to pay the difference when you file your tax return.
If you live and work in NJ all year, and do not work in NC at all, your employer should not be withholding NC tax. They should be withholding NJ tax. The ideal solution would be to get your employer to correct the erroneous withholding before the end of the year. Then your W-2 would show all your wages as NJ wages, with NJ tax withheld, and no NC income or NC tax withheld. They can make this correction, but they might tell you that they can't, either because they don't think that they can do it or because they don't want to bother. If they do make the correction, you will simply file a NJ resident tax return.
If they will not correct their error, you would have to file a NC nonresident tax return showing zero NC income in order to get a refund of the NC tax that was mistakenly withheld. The problem with that is that your W-2 will show NC wages, so you will get a letter from the NC Department of Revenue saying that your NC tax return is incorrect and you do have to pay NC tax. You would then have to try to convince the DOR that the W-2 is wrong, and you did not actually earn any income in NC. It would be a big help if you could get a letter from your employer saying that the W-2 is
wrong and you did not work in NC.
Again, I have assumed that you worked only in NJ and did not work in NC at all. If that assumption is wrong, and you actually did work in NC, even for a short time, then much of what I wrote above needs to be modified.
If you traveled to other states, technically your employer should be keeping track of which states you worked in, and how many days you worked in each state. Your W-2 should then show the amount that you earned in each state, and you would have to file a nonresident tax return in each state that you worked in. But in practical terms, if you spent only a few days in each state it might not be worth the trouble for either you or your employer. The amount of tax that you would have to pay to each state would be very small, or possibly zero.
