Federal habeas corpus is a procedure under which a federal court may review the legality of an individual's incarceration. Court is directed to issue the Writ of Habeas Corpus Ad Prosequendum as requested.Dated: JUDGE OF DISTRICT COURT. The Suspension Clause says no more than that "the privilege of the Writ of Habeas Corpus shall not be suspended, unless when in Cases of. Allen is examined as the case that firmly established that all Federal constitutional claims may be heard through the writ of habeas corpus. Therefore, Petitioner has not filed a petition seeking a writ of habeas corpus; but rather, he has elected to file a petition seeking a writ of coram nobis. This Guidebook is organized in the sequence that a habeas petition proceeds through the Court and is written in a question-and answer format. Facts in light of the evidence presented in the State court proceeding. A sample form appears below: APPLICATION FOR WRIT OF HABEAS CORPUS.