You will need to file a non-resident New York tax return and a resident New Jersey tax return. Be sure to complete your New York return first.
New York is one of a handful of states that has a “convenience of employer” rule, meaning workers must pay income tax to New York if their employer is based in the state, even if their job was done remotely. An exception is made for workers who were required by their job to work outside New York.
You will need to file a non-resident New York tax return and a resident New Jersey tax return. Be sure to complete your New York return first.
New York is one of a handful of states that has a “convenience of employer” rule, meaning workers must pay income tax to New York if their employer is based in the state, even if their job was done remotely. An exception is made for workers who were required by their job to work outside New York.
As the reply indicates, you most likely need to file a NY non resident return. You will also have to calculate NJ tax on the NY income, but NJ will give you a credit, or partial credit, for the tax paid to NY.
That said, I'm surprised that your employer did not withhold NY tax. If you did not work a single day in NY, you would not be subject to NY tax.
Here's the New York law supporting the last sentence in @Hal_Al 's answer:
"The New York adjusted gross income of a nonresident individual rendering personal services as an employee includes the compensation for personal services entering into his Federal adjusted gross income, but only if, and to the extent that, his services were rendered within New York State. Compensation for personal services rendered by a nonresident individual wholly without New York State is not included in his New York adjusted gross income, regardless of the fact that payment may be made from a point within New York State or that the employer is a resident individual, partnership or corporation."
https://www.law.cornell.edu/regulations/new-york/20-NYCRR-132.4