The answer to your question depends on the number of workdays you will actually spend in New York. If you will never set foot in New York for your work, not even for a single day, then you will owe no income tax to New York. In that case you would only need to withhold NJ taxes.
If you will perform any work within New York, then you will also have to pay NY income tax on those earnings. Depending on the amount you expect to earn in NY, you may want your employer to also withhold NY taxes.
IMPORTANT: If you perform any of your work within New York State, then you will fall under NY's "convenience of the employer" rule. That rule states that if you work partly within and partly without New York, then any work you perform remotely from without New York is taxable by New York if you are working remotely for your own convenience, rather than for that of your employer. The rule is detailed here:
https://www.tax.ny.gov/pdf/memos/income/m06_5i.pdf
NJ can tax all your income. NY can tax it as described above. If you do have to pay taxes to both states, you'll be able to claim a credit on your NJ return for the taxes paid to NY. The credit prevents double taxation, which is prohibited by federal law.
Once you determine your expected income allocation, you can submit NY Form IT-2104.1 to your employer. Here's a link to that form:
https://www.tax.ny.gov/pdf/current_forms/it/it2104_1_fill_in.pdf
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
