Q. I was just wondering which is the real adar-aleph or bais? My birthday is in adar aleph, so does that mean my birthday only comes during a leap year?
A. If you were born in a leap year on Adar Alef your birthday or bar/bas mitzvah would be on an ordinary year that day in the (single) Adar month available. On a leap year it would be the day on the corresponding Adar (Alef or Beth) you were born.
Shulchan Oruch (O.H. 55: 10) presents an interesting situation when two children, one born first on the twenty-ninth of the first Adar and the other later on the first day of the second Adar, if the year they reach bar mitzvah is an ordinary year, the one born earlier on the twenty-ninth would became of age later at the end of the month, while the one born later would reach his bar mitzvah earlier at the beginning of the month.
Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit"a