Which of the following “writs” of the High Court or the Supreme Court is sought to produce in the court…

The correct choice is: Habeas Corpus

Habeas corpus means ‘to have the body’. The court orders the person detaining someone to produce that person before it, so that the legality of the detention can be examined. Mandamus orders a public official to do a duty, quo warranto questions a person's right to an office, and certiorari quashes an order of a lower court.

Hence the answer is ‘Habeas Corpus’.