Does a landlord have to fix an AC in Ohio?
That depends, but generally no (or maybe).
As with any legal contract (lease agreement), if the landlord specifically provides for AC in the lease, then the landlord would be required to maintain it.
If it is not covered by the lease, the landlord would not have to provide AC let alone maintain it.
The Ohio Revised Code specifies that landlords have to provide heat, but doesn’t mention air conditioning.
Supply running water, reasonable amounts of hot water, and reasonable heat at all times, except where the building that includes the dwelling unit is not required by law to be equipped for that purpose, or the dwelling unit is so constructed that heat or hot water is generated by an installation
within the exclusive control of the tenant and
supplied by a direct public utility connection.