You would file non resident Ohio return since you will be taxed on that income.
@Bsch4477 So I will have to pay State taxes and Federal taxes? In Florida we only pay Federal taxes, that is why Im asking.
I disagree with @Bsch4477. There are a few states that tax remote workers (telecommuters), but Ohio is not one of them. If you are working in Florida for a company in Ohio, you do not pay Ohio tax. You should make sure that the company does not withhold Ohio tax from your pay. However, if you go to the company office in Ohio, even just occasionally or for a short time, you have to pay Ohio tax on the money that you earn for the time that you are working in Ohio.
I agree with rjs, you do not pay OH state tax exept for the days you physically work in OH. If you work even one day, in OH, you will then be required to file a non-resident OH return.
Ask you employer not to withhold either state or city income tax. Most OH employers know that they are not required to withhold OH state income tax in your situation. But, some think they are required to withhold city income tax. If that happens, you may have to file a city return to get a refund. Contact the city for a special refund form.