Extraordinary Writs aka Prerogative Writs- used for seeking Extraordinary Relief:

Extraordinary Writ:

(17c) A writ issued by a court exercising unusual or discretionary power.  Examples are writ of certiorariwrit of habeas corpus, writ of mandamus. & prohibition writ.Also termed prerogative writ.

Extraordinary Relief:

(18c) Judicial relief that exceeds what is typically or
customarily granted but is warranted by the unique or extreme circumstances of a situation. The types of extraordinary relief most frequently sought are injunctions and extraordinary writs, esp. mandamus. See INJUNCTION (order);
(writ of) MANDAMUS; PROHIBITION (writ) (2).

   Also termed prerogative writs, extraordinary writs are a subset of the class of writs, those that are to be heard ahead
of any other cases on a court’s docket except other such writs. The most common are habeas corpus, quo warranto, prohibito, mandamus, procedendo,
and certiorari.

     The due process for petitions for such writs is not simply civil or criminal, because they incorporate the presumption of nonauthority, so that the official who is the respondent has the burden to prove his authority to do or not do something, failing which the court has no discretion but to decide for the petitioner, who may be any person, not just an interested party.

     In this they differ from a motion in a civil process in which the burden of proof is on the movant, and in which there can be a question of standing.

Writ of Habeas Corpus – command that a prisoner be brought before the court to challenge the legality of their custody & demand their release

Writ of Certiorari – issued by an appellate court, directing a lower court to deliver the record in the case for review

Writ of Mandamus & Alternative Mandamus – a ‘Demand Letter” to the Defendant(s), or a writ from a Higher Court to Compel a Lower Court, Officer, or Government Body to correct a Prior Action or Failure to Act

Writ of Prohibition – issued by an appellate court to prevent a lower court from exceeding jurisdiction or to prevent a nonjudicial officer or entity from exercising a power

Writ of Consultation – issued by an appellate court ordering a lower court to proceed in a matter the lower court previously refused to hear