Since you reside in NJ, ALL your income is taxable by NJ, regardless of where you earn it.
If you never physically worked in NY during the tax year, not even for a single day, then your work income for the tax year is not taxable by NY.
NY can tax any income you earned by physically working in NY. It can also tax any income you earned remotely if (1) you worked both within and without NY during the tax year; and (2) you worked remotely from a location outside NY for your own convenience, rather than because you were required to by your employer. This is known as New York's "Convenience of the Employer" rule.
So you must file a New Jersey resident tax return in any circumstance, on which you report all your income.
If you never worked in NY but your employer mistakenly withheld NY taxes, then you'd also have to file a non-resident NY tax return, on which you would show the NY withholding but declare zero NY income. This will result in NY refunding you the incorrectly withheld taxes.
If you did perform any work within NY, then you must file a non-resident NY return (in addition to your NJ tax return) in order to report the income you earned in NY, including the income you earned remotely if you worked remotely for your own convenience.
If after reading these rules you determine that you must file a non-resident NY return in addition to your NJ return, then in TurboTax be sure to complete the non-resident NY return first, before you do your home state NJ return. That way the program will calculate an "other state credit" to apply to your NJ return for the taxes you pay to NY. This avoids double taxation.
Important: You should file NY Form IT-2104.1 with your employer ASAP. Here's a link to that form:
https://www.tax.ny.gov/pdf/current_forms/it/it2104_1_fill_in.pdf
Submission of this form will direct your employer as to what NY taxes (if any) to withhold from your pay from this point forward.
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
