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Supreme Court Justice Clarence Thomas was accepted as a Writ of Mandamus through the 11th Circuit Court of Appeals

[An 'Application' to Supreme Court Justice Clarence Thomas was accepted as a Writ of Mandamus through the 11th Circuit Court of Appeals.
This Writ of Mandamus (Application) is something Justice Thomas can rule on independently, or he can forward it to the whole of the Supreme Court.
https://www.georgiarecord.com/election-integrity/2023/10/24/breaking-11th-circuit-emergency-writ-accepted-to-hear-case-to-invalidate-fraudulent-2020-2022-elections-justice-clarence-thomas-to-rule/]

Mandamus
A (writ of) mandamus is an order from a court to an inferior government official '''ordering the government official to properly fulfill their official duties or correct an abuse of discretion. See e.g. Cheney v. United States Dist. Court For D.C. (2004). According to the U.S. Department of Justice, "Mandamus is an extraordinary remedy, which should only be used in exceptional circumstances of peculiar emergency or public importance."

Mandamus at the Federal Level
In federal courts, these orders most frequently appear when a party to a suit wants to appeal a judge's decision but is blocked by rules against interlocutory appeals. Instead of appealing directly, the party simply sues the judge, seeking a mandamus compelling the judge to correct their earlier mistake. Generally, this type of indirect appeal is only available if the party has no alternative means of seeking review.
The All Writs Act (28 U.S. Code § 1651) gave the "Supreme Court and all courts established by Act of Congress" the authority to issue writs of mandamus "in aid of their respective jurisdictions and agreeable to the usages and principles of law."
Further, 28 U.S. Code § 1361 gave federal district courts "original jurisdiction of any action in the nature of mandamus to compel an officer or employee of the United States or any agency thereof to perform a duty owed to the plaintiff."

Mandamus at the State Level
For comity purposes, state courts cannot direct a federal officer through a mandamus and federal courts likewise cannot issue a mandamus to a state officer. Rules on mandamus and similar orders vary by jurisdiction.