Praise be to Allah, and may peace and blessings be upon the Messenger of Allah.
It has been established in the authentic Sunnah that the Mahdi will appear at the end of time and fill the earth with justice and fairness after it has been filled with oppression and injustice. A number of scholars have stated that the hadiths concerning the Mahdi have reached the level of mass transmission due to their large number.
Among his characteristics is that he will be from the descendants of Fatimah, may Allah be pleased with her, and that his name will correspond to the name of the Prophet ﷺ and his father's name, as indicated by the narrations concerning him. It is important to distinguish between the Mahdi established by the Sunnah and the belief held by some sects concerning an absent person whom they claim entered a cellar or underground chamber and is awaiting his emergence; there is no sound evidence for this.
Throughout history, people have appeared claiming to be the Mahdi, some of whom were impostors. Therefore, it is not permissible to believe everyone who claims to be the Mahdi.
As for the claim that the Mahdi is already alive and has already been born, there is no authentic evidence for this. The hadiths do not specify the place or time of his birth, nor do they instruct Muslims to search for him or raise him. Rather, they state that Allah تعالى will rectify him in one night, after which the Muslims will pledge allegiance to him and unite around him.
Therefore, asserting that he has already been born or that he is currently living among people in our time is merely a claim without evidence. We do not know when he will appear, for that is part of the knowledge of Allah تعالى.
And Allah knows best.