In 2003, the 64-year-old was the first person in the history of the state to be convicted of such an offence.
A civil court in Belfast subsequently found him liable for the 1998 Omagh car bomb that killed 29 people.
The Real IRA leader has tried to appeal both rulings but without success.
This latest attempt to overturn his criminal conviction for directing terrorism in part centres around the use of S29 search warrants, which were deemed unconstituional by the Supreme Court many years after his case was determined.
His lawyers claimed this could be considered a newly discovered fact for the purpose of a miscarriage of justice application.
They say the point is so important it should be considered by the Supreme Court.
However that route has now been blocked by the Court of Criminal Appeal which has called McKevitt's application 'misconceived' in a written judgment issued today.
