There are things that can be done besides filing a direct appeal of your conviction. The most prevalent of these is filing a post conviction petition pursuant to R.C. 2953.21. This contains all the events and circumstances that occurred outside of the record. The record being everything that was taken down by a court reporter in court and all motions filed by your lawyer. Most of these events deal with ineffective assistance of counsel, prosecutorial misconduct, juror misconduct, etc. All of these claims must be based upon the Federal Constitution. If they are not they are not claims for the post conviction petition. This must be filed within one year of the transcripts being filed in your direct appeal.
All of the fact claims must be supported by affidavits. An affidavit is a sworn statement that is notarized by a licensed notary public. Other information can be included by an affidavit must be attached to the petition.