  The first main result of this paper is to build the first and second
restricted cohomology groups for restricted Lie superalgebras in characteristic
$p\geq3$, modifying a construction by Yuan, Chen and Cao. We will explain how
these groups capture some algebraic structures, such as extensions and
derivations. Further, we apply this construction to classify $p$-nilpotent
restricted Lie superalgebras up to dimension $4$ over an algebraically closed
field of characteristic $p\geq3$.
