  In this paper, we classify irreducible representations of affine group
superschemes over fields $F$ of characteristic not two in terms of those over a
separable closure $F^{\mathrm{sep}}$ and their Galois twists. We also compute
the division superalgebras of their endomorphisms mainly when they are central.
Finally, we give numerical conclusions for quasi-reductive algebraic
supergroups under certain conditions, based on Shibata's Borel--Weil theory for
split quasi-reductive algebraic supergroups.
