Yes. Most (or all) states also have procedures that allow citizens to challenge the placement of a candidate on the official ballot who is not eligible to hold the office for which the candidate has filed. See e.g. Minnesota's. This would be used to strike someone from a presidential ballot if the would-be candidate (among other ineligibilities):
- is under the required age,
- is not a natural born citizen, or
- having previously taken an oath, as a member of Congress, or as an officer of the United States, or as a member of any state legislature, or as an executive or judicial officer of any state, to support the Constitution of the United States, has engaged in insurrection or rebellion against the same, or given aid or comfort to the enemies thereof (if the arguments of the challengers in several current petitions is correct).
As for whether section 3 of the the 14th amendment in fact renders Trump ineligible, that is the topic of ongoing litigation, as well as William Baude and Michael Stokes Paulsen's article, "The Sweep and Force of Section Three" (forthcoming 2024) 172 U. Pa. L. Rev. The meaning of "enemies thereof" is also discussed at another Q&A on this site: In Section 3 of the 14th Amendment, what does "enemies thereof" refer to?