State tax filing

Some companies that do not have a physical presence in another state may not withhold state taxes from the state where you are working remotely.

You need to ask your employer if they are going to withhold NY state and NYC taxes from your wages.  If they are not then you need to pay estimated taxes to both NY state and New York City.

Go to this New York state website for how to make estimated tax payments - https://www.tax.ny.gov/pay/ind/pay-estimated-tax.htm