Let me know what rights I have has a landlord to refund a deposit.

Unless your lease has a provision allowing for a cancellation, your tenant has manifested an intent to breach the agreement. Under Ohio law you are obligated to try to re-lease the space to mitigate your damages. If you are unable to find a substitute tenant, then you may withhold the deposit and sue for whatever damages you suffer over the next year until the space is leased.

However, as a practical matter, if you have a nice property that you can rent quickly, and you wish to avoid acrimony with your current tenant, you can also negotiate a settlement whereby you grant a partial refund of the deposit and release them of their future obligations under the lease.

Ultimately, you should proceed as you are most comfortable and, if you have additional questions, reach out to a local real estate attorney who can advise you of your rights. Good luck.