The following are some of the publications that can help you keep up to date with current developments in Ohio law.
Domestic Relations Journal of Ohio by 
Probate Law Journal of Ohio
It is logical that law reviews published by Ohio law schools often have articles pertaining to Ohio law.
Find Ohio law review articles on Westlaw: All Ohio Law Reviews and Journals or Lexis Advance - prefilter by Ohio and Secondary Sources and then postfilter by Law Reviews.
The following are law reviews available on their school's websites: