You will have to file a 2nd City return, for the city your employer withheld for, to get a refund. Ask your employer to stop withholding for that city. You should contact that city, as many have a special form for a refund in this situation.
During Covid, Ohio allowed cities to collect tax, from the work city, even when the employee worked from home in a different city. That ruled expired 12-31-21. Your employer may not be aware of that expiration.
Reference:
https://frostbrowntodd.com/ohio-tax-talk-adjusting-to-the-latest-telework-tax-rules/
https://taxnews.ey.com/news/2021-1235-ohio-governor-lifts-covid-19-emergency-order-and-starts-clock-....
