City Tax

I am a home health aide in Ohio. I work in one city where my clients are, and also where I reside in, and the office that my job is based out if is in another city, over an hour away. I never go to this office except for once a year to update my paperwork, fingerprints, CPR certification, etc. Other than that my timesheets are faxed every week and I dont go there ever. Obviously I pay Ohio state tax, but I was looking at my paystub and I'm paying taxes for both cities. Is this correct? Im just not super familiar with the city tax laws in Ohio, and couldn't find anything about this question in particular!

Thanks!!!