It won’t even get into district court, let alone an appellate court.
The Courts ENTIRELY lack jurisdiction, for several reasons, not the least of which is that there is no law that can be said to have been broken. This is a political issue, not a legal one.
Just one counterexample ...
South Carolina Title 7 - Chapter 11
Section 7-11-20(B)(2)(b)(b) the state committee of the party shall set the date and the filing requirements, including a certification fee. Political parties must verify the qualifications of candidates prior to certifying to the State Election Commission the names of candidates to be placed on primary ballots. The written certification required by this section must contain a statement that each certified candidate meets, or will meet by the time of the general election, or as otherwise required by law, the qualifications in the United States Constitution, statutory law, and party rules to participate in the presidential preference primary for which he has filed. Political parties must not certify any candidate who does not or will not by the time of the general election meet the qualifications in the United States Constitution, statutory law, and party rules for the presidential preference primary for which the candidate desires to file, and such candidate's name must not be placed on a primary ballot.