Time limitations for Post-Conviction relief are found in MS Code Ann 99-39-5(2):

A motion for relief under this article shall be made within three (3) years after the time in which the petitioner’s direct appeal is ruled upon by the Supreme Court of Mississippi or, in case no appeal is taken, within three (3) years after the time for taking an appeal from the judgment of conviction or sentence has expired, or in case of a guilty plea, within three (3) years after entry of the judgment of conviction. Excepted from this three-year statute of limitations are those cases in which the petitioner can demonstrate either:
(a)
(i) That there has been an intervening decision of the Supreme Court of either the State of Mississippi or the United States which would have actually adversely affected the outcome of his conviction or sentence or that he has evidence, not reasonably discoverable at the time of trial, which is of such nature that it would be practically conclusive that had such been introduced at trial it would have caused a different result in the conviction or sentence; or
(ii) That, even if the petitioner pled guilty or nolo contendere, or confessed or admitted to a crime, there exists biological evidence not tested, or, if previously tested, that can be subjected to additional DNA testing that would provide a reasonable likelihood of more probative results, and that testing would demonstrate by reasonable probability that the petitioner would not have been convicted or would have received a lesser sentence if favorable results had been obtained through such forensic DNA testing at the time of the original prosecution.

§ 99-39-5. Grounds for relief; time limitations; “biological evidence” defined.