Q. If someone has yortzait in Ador, (father died in a single month year) and when they are two Adors he keeps both yortzaits for kadish. Which is the most important for the purpose of making a siyum?

A. Shulchan Aruch (O.H. 568: 7) maintains that the second Adar preempts the first for fasting on a yortzait, for someone while the Remoh (ibid,) sustains the first Adar, but recommends to keep both.
While Mishna Berurah (ibid. 41) follows the Remoh, Chasam Sofer (O.H. 163) and other Poskim maintain that the second Adar is primordial in reciting Kadish.
The minhag today is to recite kadish on both and to lead the service when not in conflict with others, also on both days.
Horav Shlomo Miller’s Shlit”a opinion is that if possible he should make a siyum on both days; otherwise he should choose the second Adar.(See also question 996.)

Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit”a