  The purpose of this paper is to study minimal modular extensions of braided
fusion categories doing emphases in minimal modular extensions of
super-Tannakian fusion categories. We define actions of finite super-groups on
fermionic fusion categories and spin-braided fusion categories. Similar to the
case of groups, our motivation came from the study of fusion categories
containing the representation category of a super-group. We develop many analog
results to the Tannakian case, including cohomological obstructions, relation
with braided $G$-crossed categories and minimal modular extensions. We apply
the general results to the construction and classification of minimal modular
extensions of super-groups and braided fusion categories. In particular, we
exhibit some examples of braided fusion categories without minimal modular
extensions.
