If a boy in the synagogue claims that he has reached the age of Bar-Misva, the others should not rely on this claim to count him toward a Minyan, or to allow him to serve as Hazzan. He can be counted only if his father testifies that he reached the age of thirteen, or if somebody testifies that this boy's father said this about the boy. The boy's testimony about his age should not be accepted. Even if he is wearing Tefillin, this does not prove that he is already a Bar-Misva, for many communities have the custom that boys begin wearing Tefillin at some point before becoming Bar-Misva.
If, however, this boy is needed for the Minyan, and without him the Minyan will be lost, then his claim may be trusted with respect to his inclusion in a Minyan. Even in such a case, however, he should not be allowed to serve as Hazzan.
This is the ruling of Hacham Ovadia Yosef, though others disagreed. Rav Shlomo Zalman Auerbach (Jerusalem, 1910-1995) contended that the child may be trusted because he is unlikely to lie, given the possibility of verifying his claim. A person can be assumed to tell the truth about something which is easily verifiable, as he fears being viewed as a dishonest person. Hence, in Rav Shlomo Zalman's view, the boy can be assumed to be telling the truth.
In any event, we follow Hacham Ovadia's position, and thus a boy cannot be assumed to be a Bar-Misva based solely on his claim, unless there is no Minyan without him.