Yes. You would file a New York nonresident return regardless of what your employer withheld for NY because you worked some days in New York. Since your employer withheld almost no New York tax, you will owe NY and get an excessive refund from NJ.
New Jersey will give you a credit for tax paid to NY PLUSis you had NJ tax withheld on some or all of that income.
You can file both returns and pay NY after you get your NJ refund. The New York filing deadline is April 18.
New York has a “convenience of the employer rule,” meaning if you telecommute for your own convenience, you are subject to NY tax.
Your wages are probably 100% New York, though you may be able to allocate days worked outside NY as non-NY income. Each case it different. It depends on the number of days worked outside NY and your working arrangements.
NY is very aggressive about taxing telecommuters. Taxpayers have lost cases when the facts were clearly in their favor.
The best thing is to get would withholding fixed.
TurboTax has an excellent discussion about the “convenience of the employer” rule including posts by a former NY state auditor at “I work for a NY company, remotely from NC. I spent 1 day in 2017 on site, but my W-2 has full salary...
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