In the context of mandamus from a United States Court of Appeals to a United States District Court, the Supreme Court has ruled that the appellate courts have discretion to issue mandamus to control an abuse of discretion by the lower court in unusual circumstances, where there is a compelling reason not to wait for an appeal from a final judgment. This discretion is exercised very sparingly. It is exercised with somewhat greater frequency, although still sparingly, in the context of discovery disputes involving privileged materials, since a district court order erroneously forcing the disclosure of privileged material may never be remediable through a later appeal. In the case In Re Electronic Privacy Information Center (2013), privacy advocates sought a writ of mandamus directly from the Supreme Court to halt the National Security Agency's bulk phone record collection program. The Supreme Court denied the petition. More recently, the Supreme Court sided with the US Government and issued a writ of mandamus related to discovery in a court case involving the rescinding of the Deferred Action for Childhood Arrivals policy.

Is it true that does the supreme court have the power to issue a writ of mandamus?
yes