Q. I have Yohrzait on Purim Katan for my mother A'H. The minhag of our family is to fast on a Yohrzait for parents, but on this occasion I was told I should not fast. Would it be correct then to fast the on Taanit Esther, the day before, since it is called after all a Taanit?
A. Indeed Shulchan Aruch (O.H. 697: 1) rules that one does not fast on Purim Koton
On question 3526 in regard to Yohrzait fasting on Tu Bishvat, and if one could keep the Yohrzait Taanis next day, we wrote: Shulchan Aruch (O. H. 568: 9) rules that if the day of Yohrzait for one's father fell on Shabbos or Rosh Chodesh, the fasting should be done next day. However, Remah adds that the minhag is not to fast at all.
Piskei Teshuvos (ibid) quotes that one may comply earlier with the visit to the Kever on Friday. However, as mentioned the minhag is not to fast at all.
Rabbi A. Bartfeld as revised by Horav Dovid Pam, Horav Aharon Miller and Horav Chanoch Ehrentreu Shlit'a