What is the method and authority through which a person can report themselves to have the death penalty applied, while maintaining privacy?

If the reality is that this person did not commit sodomy, then there is no prescribed punishment (hadd) for him in Islamic law, and he should abandon thinking about this matter. We advise him not to commit murder, for it is a grave crime that constricts the religion of its perpetrator, in accordance with the Prophet's (peace and blessings be upon him) saying: "A believer remains within the latitude of his religion as long as he does not shed unlawful blood."