In a leap year, Purim is marked in the second Adar. In the first Adar, the 14th is noted as Purim Katan and the day after, as Shushan Purim Katan. The implications are limited (basically) to slight liturgical changes and the possibility of a little more celebration.
If, as this article suggests, the reasoning is that the actual Purim event happened in the first Adar of a leap year
Others, however, explain that the Talmud is actually stating that Haman’s lottery fell out on the 12th month, Adar I in a leap year. {See, for example, Yaarot Devash 2:7; responsum Chatam Sofer, Orach Chaim 163.}
then why wouldn't there also be a ta'anit Esther Katan on the 13th of Adar 1? I'm not suggesting any particular practice or ritual implications, but if we draw the parallels between the two months, why stop short of including the (commemoration of the )fast preceding the event?