The Texas Supreme Court and Court of Criminal Appeals have appellate jurisdiction, which means they have the authority to do what?

They have the power to review and alter lower court results.

Explanation:

The Texas Court of Criminal Leads is the court of the last line of defense in Texas, us, for all capital cases. The court, located in Downtown Austin's Supreme Court Tower, is consisting of a judge in the case and eight jurors. The Court has several exclusive power to grant a person who's been convicted of a crime (which would be a punishable crime or incarceration in the department of Juvenile justice) the habeas corpus and give reviews court results.