Your employer is now withholding correctly. If you as a non-resident of New York never physically work in New York State, not even for a single day, then your income is not subject to NYS income tax. However, since your employer did mistakenly withhold some NYS tax, in order to obtain a refund of the withheld amount you'd have to file a non-resident NYS return on which you report the withholding but allocate zero income to NYS.
The income you earned as a KY resident from a KY employer is not subject to NY income tax, as long as you never worked remotely from a NY location for that employer.
TurboTax has a help article on this:
Is my remote income taxable in New York State? (intuit.com)
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
