Generally, if you have been convicted of a sex crime, you are going to end up on the sex offender's registry list. This list will have your name and what your crimes are. You have to keep it updated so that it has your current address on it as well as other pertinent information. However, there are some people who may be on the list who really shouldn't be. That can include teenagers who were having sex with their partner while their partner was underage. For example, in some states, someone who has just turned 18 who is in a consensual relationship with a 16 year could be arrested for statutory rape and their name could end up on the sex offender's registry list. If you are in a situation where you are on the list wrongly, you may want to know what you can do to get off the list.
See a Lawyer
The first thing you are going to need to do is to see a sex crime attorney. They are going to be familiar with all the ins and outs of the laws around sex crimes and which laws may affect you and which may not, and how they may affect you. In your hypothetical case of being on the list because of statutory rape, your state may have laws around the age differences between you and your partner. If you were barely 18, but your partner was 16, there may be fewer problems than if you were 18 but your partner was 15 or younger. The lawyer you go see will help you figure out if that is going to be a problem for you.
File the Appeal
You and your lawyer are going to have to file an appeal at the state level to get your name off the list. That appeal will either go to a judge or to a committee from the agency who oversees the sex offenders registry in your state. Once you have filed, you may have to appear in person and answer questions from the court or the committee as to why you are on the list, what you have done since you've been on the list, how you may have been rehabilitated, etc.
If you have been put on the sex offender's registry list and you believe that you are on there wrongly, there are things that you can do that may be able to get you off the list. Reach out to an attorney for more guidance.