The Hastings Constitutional Law Quarterly has this very detailed account of how Ohio has tried to keep minor parties off its ballots, for over 100 years. The article is by Law Professor Mark R. Brown, who has been active in ballot access litigation in Ohio for almost twenty years.
Ohio was unique among the populous states in the 1910’s for its severe ballot access laws. The main problem was that in 1908, Ohio raised the definition of a qualified party to a group that had polled 10% of the vote, at a time when virtually no other states had such a severe definition. It was the only populous state that had no statewide minor party or independent candidates on the ballot in 1918, nor 1922, nor 1930, for example.
The main part of the article concerns the battles in this century, particularly in 2014, when a federal court ordered the Libertarian Party put on the ballot but then Republican officials still managed to keep the party’s gubernatorial candidate off the party’s primary ballot. Because the vote test required 2% (for 2014 only; the ongoing vote test was to be 3%), and only the gubernatorial election counted, this meant that the Libertarian Party had no gubernatorial candidate and thus fell off the ballot. The article also explains the attempts by Republican officials to prevent recognizing the Libertarian Party after the 2016 election, even though its presidential nominee, Gary Johnson, on the ballot as an independent, had met the 3% vote test.