This is correct. West Virginia and Kentucky are reciprocal states, which means you are taxed where you live: Kentucky. You will want to file a West Virginia special nonresident return in order to get back the taxes you paid to WV. However, you will use that refund to pay your KY balance due.
You may file a form with your WV employer so that KY taxes are withheld instead of WV taxes. Here is an FAQ which gives more information on reciprocal states and the form you must file: https://ttlc.intuit.com/replies/4776822
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