If you as a non-resident of NY never physically work within NY - not even for a day - then your income from that work is not taxable by NY, and your employer is not obligated to and should not withhold NY taxes. But if they do anyway, you'll have to file a non-resident NY tax return on which you allocate zero income to NY, in order to receive a refund of those withholdings.
As a resident of MD, your income is 100% taxable by MD, regardless of its source. So ideally, your employer will withhold MD taxes for you. If they don't, you will have to make quarterly estimated tax payments to MD.
If you do travel to NY and do any work from a NY location, then that portion of your income would be taxable by NY.
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
