A non-resident of New York who never physically works in New York, not even for a single day, has no income tax obligation to the state of New York for their work earnings. New York's "convenience of the employer" rule does not apply in such a situation.
Unfortunately, the NY taxes already withheld from your pay have by this time been deposited with the state. In order to claim a refund of the incorrectly withheld taxes, you'll have to file a non-resident NY tax return at year's end, showing the NY withholding but claiming zero NY income.
Your income is 100% taxable by your resident state of VT. Your employer should be withholding VT income tax for you. Since no VT taxes have been withheld from your pay this year, you may want to make an estimated tax payment to VT in order to reduce or avoid any penalties. If your employer does not withhold VT income tax for you going forward, then you must make quarterly estimated tax payments to VT. See this reference for more info:
https://tax.vermont.gov/individuals/estimated-income-tax
Finally, you should file NY Form 2104.1 with your employer, declaring your non-residence in NY and stating that zero percent of your work services will be performed in NY. Hopefully this will get your employer to cease withholding NY taxes. 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.
