The only way I know of to remove a sitting Senator is for the Senate to do it. The House and the Senate are not subject to impeachment but have the authority to remove members. Back in the sixties Harlem Congressman, Adam Clayton Powell, was removed for his corruption. His constiuents merely reelected him and the next House allowed him to stay.
Now it would be incumbent on us to make enough of a stink that the Senate would do it should the proof be there that he is ineligible. Or he could be sued for fraud or have criminal charges filed against him leading to the same results.
This issue could have never arisen in the past since there was no Treason media able to cover up such crimes so effectively.
The Founding Fathers must be turning in their graves.