It was indeed a presidential candidate. Hassan v Colorado, 2012.

… as the magistrate judge’s opinion makes clear and we expressly reaffirm here, a state’s legitimate interest in protecting the integrity and practical functioning of the political process permits it to exclude from the ballot candidates who are constitutionally prohibited from assuming office. See generally Munro v. Socialist Workers Party, 479 U.S. 189, 193-95 (1986); Bullock v. Carter, 405 U.S. 134, 145 (1972).

Also, you’ve got a typo. Ineligible. Illegible means something written so poorly that it cannot be understood.