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Jones has been in prison since 2005, serving a life sentence.
Jones has previously filed motions to have his case re-heard and they have been denied. His first appeal was filed in December 2009.
His appeal said his attorneys should have presented more evidence to show the killing of his grandfather was in self-defense.
His appeal was rejected last year. The Mississippi Court of Appeals denied his request for a rehearing earlier this year, which the Mississippi Supreme Court granted Thursday.
Jones, who was 15 at the time, testified he was in the kitchen making a sandwich when his grandfather came in and cornered him. He claimed he stabbed his grandfather out of self-defense.
He is currently in the Mississippi State Penitentiary at Parchman.