February 5 was the Ohio deadline for candidates seeking a place on a primary ballot this year. This story mentions the statewide candidates who filed. It appears the Libertarian Party is running a full slate for the statewide partisan races (there is no U.S. Senate race this year in Ohio). The Green Party has only one statewide entry, a joint ticket for Governor/Lieutenant Governor.
Although no Socialist Party filed for statewide office, a Socialist filed to run for U.S. House in the Ninth District. It is not known whether anyone filed to run in the Constitution Party primary.
Ohio permits write-ins in primaries, so parties could potentially run more candidates if they obtain enough write-ins in the primary. Statewide write-in candidates need 500 votes, and district candidates need 25. The primary is May 6.