In such criminal cases where the defendant has been adjudicated guilty by the trial court he may, if no motion for a new trial is filed within 10 days after the last day on which a motion for a new trial could have been filed or within 10 days after the ruling of the trial court upon a motion for a new trial, duly filed and ruled on adversely to defendant, file with the clerk or the trial judge of the court wherein such defendant was adjudicated guilty and sentenced a petition in writing, sworn to and subscribed by said defendant, stating that the defendant desires to take an appeal under the provisions of this division. Such petition must identify the style of the case, the offense for which the defendant was convicted, the plea made by the defendant, the date of the adjudication of guilt, the sentence and the punishment therefor and the name of the court imposing such punishment, together with the name of the trial judge. Such petition shall also contain the full name of the defendant, together with a statement that he desires to appeal either from the judgment of conviction or from the adverse ruling on the motion for a new trial, or both. Such petition must contain an averment that the defendant is without sufficient funds, and has no reasonable way to procure the same, to pay the court reporter all of his lawful fees for transcribing the evidence and other proceedings had at the trial of said case, or the fees of the clerk for preparing the record on appeal. In such other cases, including habeas corpus and coram nobis, which are related or collateral proceedings to a conviction of a criminal offense and which proceedings involve the life, liberty or property of a person convicted of a crime, the person convicted may, within 10 days after a judgment or order disposing of the proceedings adversely to said person, file with the clerk or the trial judge of the court making said order a similar petition describing and identifying the proceeding and stating the desire of the petitioner to appeal under the provisions of this division.