New York's law regarding the "other state credit" is that the credit is allowable "only for the portion of the tax that applies to income sourced to and taxed by the other taxing authority while you were a New York State resident."
https://www.tax.ny.gov/pdf/current_forms/it/it112ri.pdf
Since none of your income while you were a New York State resident was taxable either by KY or by NJ, there is no other state credit available to you on your NYS part-year resident return.
However, you should be eligible to claim an "other state credit" on your KY part-year resident return, since you did have income taxable by other states during your period of KY residency. Note that your "other state credit" cannot exceed the tax you would have owed had the income been taxable only by KY.
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
