On April 2, the U.S. Supreme Court refused to hear Tripp v Scholz, 17-1129. This was an Illinois Green Party case that challenged the Illinois requirements for nominees of unqualified parties to get on the ballot for state legislature. They are so severe, no third party candidates appeared on the Illinois ballot in 2016 for the legislature.
The U.S. Supreme Court has not granted any cert petition filed by a minor party or an independent candidate, involving ballot access, since 1991. Although the Court granted Burdick v Takushi in early 1992, that case (involving write-in votes) was filed by a Democratic Party voter and did not concern third parties or independents directly.
The case that was granted in 1991 was Norman v Reed, an Illinois case.