  The main goal of this paper is to develop the structure theory of Hom-Lie
superalgebras in characteristic 2. We discuss their representations, semidirect
product, $\alpha^k$-derivations and provide a classification in low dimension.
We introduce another notion of restrictedness on Hom-Lie algebras in
characteristic 2, different from one given by Guan and Chen. This definition is
inspired by the process of queerification of restricted Lie algebras in
characteristic 2. We also show that any restricted Hom-Lie algebra in
characteristic 2 can be queerified to give rise to a Hom-Lie superalgebra.
Moreover, we develop a cohomology theory of Hom-Lie superalgebras in
characteristic 2, which provides a cohomology of ordinary Lie superalgebras.
Furthermore, we establish a deformation theory of Hom-Lie superalgebras in
characteristic 2 based on this cohomology.
