Tex. Civil Practice and Remedies Code § 30.016

(a) In this section, "tertiary recusal motion" means a third or subsequent motion for recusal or disqualification filed against a district court, statutory county court, or business court judge by the same party in a case.

(b) A judge who declines recusal after a tertiary recusal motion is filed shall comply with applicable rules of procedure for recusal and disqualification except that the judge shall continue to:

(1) preside over the case;

(2) sign orders in the case; and

(3) move the case to final disposition as though a tertiary recusal motion had not been filed.

(c) A judge hearing a tertiary recusal motion against another judge who denies the motion shall award reasonable and necessary attorney's fees and costs to the party opposing the motion. The party making the motion and the attorney for the party are jointly and severally liable for the award of fees and costs. The fees and costs must be paid before the 31st day after the date the order denying the tertiary recusal motion is rendered, unless the order is properly superseded.

(d) The denial of a tertiary recusal motion is only reviewable on appeal from final judgment.

(e) If a tertiary recusal motion is finally sustained, the new judge for the case shall vacate all orders signed by the sitting judge during the pendency of the tertiary recusal motion.