An Ohio Notice of Furnishing isn't necessarily filed, instead, it's just sent to the appropriate parties in order to be effective. These parties include the property owner and the GC if you didn't contract directly with the GC. The notice should be sent by certified mail, registered mail, overnight delivery, or it can also be personally served by the county sheriff.
This should be sent within 21 days of first furnishing labor or materials to the project if a Notice of Commencement (NOC) has been filed. If the NOC was filed late, the Notice of Furnishing will need to be sent within 21 days from when the NOC was filed.
Here are some additional resources you may find helpful: