"I went to KY, where I have a permanent home..."
If your main, permanent home (your domicile in tax terminology) was in KY all of 2020, then you would file taxes as a resident of KY and a non-resident of both NY and NJ.
A part-year resident is a person who moves their domicile from one state to another during the tax year. A taxpayer can have only one domicile at a time.
These definitions may help you:
https://www.tax.ny.gov/pit/file/pit_definitions.htm
If the above scenario is correct, you'd be able to claim an 'other state credit' on your KY return for taxes you paid to NY and NJ on the portion of your income that was taxable by either state respectively and also by KY.
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
