If you are a resident of NJ and you never physically work within New York, not even for a single day, then your work income is not taxable by NY and you should ask your employer to withhold NJ taxes only from your pay.
If you work both within and without New York during the year, then the income you earn from the work you perform within NY is taxable by NY. In this situation you would also be subject to NY's convenience of the employer rule. That rule states that if you work remotely for an NY employer from an out of state location, then your remotely earned income is taxable by NY if you are working remotely for your own convenience, rather than because you are assigned or required to by your employer.
You will find New York's employer withholding rules for non-resident employees on page 45 of this reference:
https://www.tax.ny.gov/pdf/publications/withholding/nys50_1223.pdf
Here is a link to NY Form IT-2104.1, which is referred to in the withholding guide:
https://www.tax.ny.gov/pdf/current_forms/it/it2104_1_fill_in.pdf
And here is a link to New York's tax memorandum on the "convenience of the employer" rule:
https://www.tax.ny.gov/pdf/memos/income/m06_5i.pdf
@Christopher773
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
