Question
Would it be permissible to say Selichot for a fast day before with a minyan before mincha ketana?
Answer
ב"ה
Shalom
If you are talking about saying Selichot on the Fast day, before mincha instead of Shacharit., you may do so. Rav Ovadya Yosef zt"l , wrote (שו"ת יחווה דעת חלק א סימן מו) in regard to the Selichot before Rosh Hashana that if one cannot get up early in the morning to Selichot, he may do so before Mincha.
But of course, they should be said with a minyan on order to allow the sying of the 13 middot of Rachamim.
All the best
Happy Purim