If the conviction was due to some sort of DNA, perhaps the Georgia Innocence Project can help
www.ga-innocenceproject.org. After conviction, the defendant has right to file a motion for new trial withing 30 days of conviction.
Also defendant feels there was a substantial denial of his/her Constitutional Rights then he/she can file a writ of habeas corpus in the county of incarceration. For a conviction for a felony it must be filed within 4 years of conviction.