It is a lot simpler when this is actually during the election and/or the immediate aftermath before a candidate is seated. And it also heavily depends on what office this is for. When someone is holding office unlawfully - not elected, fraud, or some other illegal means - then you can file what is called "quo warranto" to have a judge remove them. However, you cannot quo warranto a congressman/senator/president/vice president. Because the constitution controls.

Art. I § 5 cl. 1 "Each House shall be the Judge of the Elections, Returns and Qualifications of its own Members"

You're not going to find house or senate races where courts have unseated a sitting congressman because the congress itself deals with that. Likewise, with the electoral college/count/certification process, it is both houses of congress that deal with choosing the executive.

You can find cases dealing with recounts, or other impermissible acts before or during the election. But for the most part, all the cases where courts removed fraudulently elected officials are outside the bounds of congress or presidency.

Its a cluster. Our system is based on people doing the right thing. We know that isn't happening.