I have lost my appeal in federal court. Can I ask the supreme court to hear my case.

If you have lost your appeal in federal court, you have ninety days to ask the United States Supreme Court to hear your case by filing a Petition for Writ of Certiorari. Keep in mind, however, that the Supreme Court agrees to hear less than one percent of the cases it is asked to hear and usually those cases involve important constitutional issues that have applicability to numerous cases rather than just one individual case.