In particular, section 3 of the 14th amendment reads:

No person shall be a Senator or Representative in Congress, or elector of President and Vice President, or hold any office, civil or military, under the United States, or under any state, who, 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, shall have engaged in insurrection or rebellion against the same, or given aid or comfort to the enemies thereof. But Congress may by a vote of two-thirds of each House, remove such disability.

This was passed after the civil war as a means of ensuring that confederates weren’t allowed to hold office.

There are modern examples as a result of the Jan. 6 2021 insurrection as well.