You will not be subject to NY City income tax, since you are not a resident.
As to NY state, it depends on more info. If you work outside the state as a job requirement, you are only subject to New York State income tax on the days you work in New York. But if you work outside New York for your own convenience, you are subject to New York State income tax on all your income. You should discuss with your employer whether they intend to withhold NYS tax. If they do, you'll have to file a non-resident NYS return, either to get a refund or to report the income.
Here's a link to New York's memorandum on its "convenience of the employer" tax doctrine regarding non-resident telecommuters: https://www.tax.ny.gov/pdf/memos/income/m06_5i.pdf
Also, see this more recent discussion, wherein the poster says it requires at least 1 day in NY to be subject to NYS income tax, even when it's for your own convenience. https://ttlc.intuit.com/community/state-taxes/discussion/re-i-work-for-a-ny-company-remotely-from-nc...
