@smac77 --
Your employer is withholding correctly. As an Ohio resident you are exempt from KY state income tax on your wages or salary, due to reciprocity. However the reciprocal agreement between the two states does not apply to local KY taxes. If you live in an Ohio city with a local tax, it's possible that it may give you a credit for the local taxes you paid to KY. It depends on your home city's tax rules. But the local KY taxes you paid are not refundable.
For others who may be reading this thread: if a KY employer mistakenly withholds KY state income tax from the pay of a resident of a reciprocal state, then that taxpayer may request a refund by filing KY Form 740-NP-R. Here's a link to that form:
https://revenue.ky.gov/Forms/Form%20740-NPR%202023.pdf
**Answers are correct to the best of my ability but do not constitute tax or legal advice.