Ideally, your employer will handle it with KY Dept. of Revenue (DOR) and give you your money back.
2nd choice is, as HACKITOFF said, is get a corrected W-2 from your employer and then file back state returns for refunds. KY has a simple form for this type of refund https://revenue.ky.gov/Forms/40A100.pdf
Even without a corrected W-2, you should apply to DOR for refund(s). You can expect DOR to require some kind of proof that you didn't work in KY.
