AFTER YOUR CASE IS OVER. Even when your court case is concluded and your appeals are done, there are still some filings and some hearings that can happen.
MODIFICATION. In some cases, you may want to go back after you've served part of your sentence and ask that the Judge change something in the sentence. This is not always permitted, especially if you took a specific sentence as part of a plea agreement, but in many cases there are things that the Judge would be allowed to change. You should talk with a lawyer before you ask to modify your sentence to see if this is possible in your case.
POST-CONVICTION RELIEF. Post-Conviction Relief is a process that allows you to go back to the trial court after your case is over and ask for a new trial on the basis that your constitutional rights were violated in the first trial, your lawyer didn't do their job properly, or that there is newly discovered evidence that shows you are innocent. This is like an appeal in some ways, except you are appealing to the original trial court in your case. The big difference between PCR and an appeal is that you can put new information before the Judge that was not discussed in your original trial or as part of your original appeal. If you cannot afford an attorney, you are entitled to have court appointed counsel help you with a Petition for Post-Conviction Relief.