R.I. Gen. Laws § 9-21-6: Allowance of appellate proceedings after time expired.

When any person is aggrieved by an order, decree, decision, or judgment of the district court or of any probate court or town council from which an appeal or other review is available in the superior court and, because of accident, mistake, unforeseen cause, or excusable neglect has failed to claim his or her appeal, the superior court, if it appears that justice so requires, may, upon petition filed within ninety (90) days after the entry of the order, decree, decision, or judgment, allow an appeal to be taken and prosecuted upon such terms and conditions as the court may prescribe.