It depends. The earned income credit is based on the income earned for the year. You must have income to receive earned income tax credit. However, there are some federal rulings that State of Ohio conformed such as Covid-19 Tax Relief. The Ohio IT1040 has refundable credits and non-refundable credits (Schedule E of Ohio IT 1040).
For the Earned Income Credit, Ohio conforms to the Federal Covid rules. That is, if your federal EIC is based on 2019 Earned income, rather than 2020 income, your Ohio EIC will also be based on 2019 income.
Technically the Ohio EIC is a straight forward percentage of the federal EIC (usually 30%, but less for higher income people).
The reason you're not getting a refund on the Ohio return is that Ohio's EIC is non refundable. That is, it can only be used to lower you Ohio income tax. Once your tax gets to zero, the rest of the Ohio EIC is NOT refunded to you.