My son receives Social Security survivor benefits due to his father’s unexpected passing, do I use that as a death Benefits deduction on my Ohio State taxes?

No.

Do not enter the SSA1099 for your child on your own tax return.   Someday if the child has other income  (after school job, etc.) and is filing a tax return, for that tax year he will need to include the SSA1099 on his own return.  Until then, it does not get entered anywhere.

The OH death benefit deduction is to remove income taxed on the federal level. Since the income is not included in the federal, the deductions isn't used on the state.

Reference:

OH instructions

I am very sorry for your loss.