The petition for appeal to the Supreme Court shall be filed with the Clerk of the Supreme Court. The Clerk shall endorse thereon the day and year he received it and shall refer it to one or more justices of the Supreme Court as the Court shall direct. A petition shall, for the purposes of § 8.01-671, be deemed to be timely filed if it is mailed postage prepaid to the Clerk by registered or certified mail and if the official postal receipt therefor is exhibited upon the demand of the Clerk or any party and it shows mailing within the prescribed time limits.