If a boy was born in Adar during a regular, twelve-month year, and the year of his Bar Misva is a leap year, when there are two months of Adar, he becomes Bar Misva in Adar Sheni. Halacha views Adar Sheni as the actual month of Adar, and it is therefore in Adar Sheni when a boy born in Adar thirteen years earlier becomes a Bar Misva.
The Shulhan Aruch (55:10) famously addresses an intriguing case involving twins born during a leap year who become Misva during a regular twelve-month year. The particular situation he discusses is when the older twin exits the womb in the final moments of 29 Adar Rishon, and the younger twin is born when it is already 1 Adar Sheni. If, thirteen years later, there is only one Adar, then the younger brother will become a Bar Misva nearly one month earlier than his older twin. The older brother was born on 29 Adar Rishon, and thus he will be considered a Bar Misva according to Halacha only on 29 Adar. The younger brother, however, who was born on the first day of Adar Sheni, becomes a Bar Misva on the first day of Adar four weeks before his older brother! This is an especially fascinating situation, where a boy becomes a Bar Misva nearly a month before somebody born a few moments before him.
Summary: If a boy was born in Adar during an ordinary twelve-month year, and the year of his Bar Misva is a leap year, he becomes Bar Misva during Adar Sheni. If a boy was born on 29 Adar Rishon, and the year of his Bar Misva is an ordinary twelve-month year, he becomes Bar Misva on 29 Adar, yet a boy born one day after him, on 1 Adar Sheni, will become Bar Misva four weeks earlier, on 1 Adar.
