  Suppose the ground field $\mathbb{F}$ is an algebraically closed field
characteristic of $p>2$. In this paper, we investigate the restricted
cohomology theory of restricted Lie superalgebras. Algebraic interpretations of
low dimensional restricted cohomology of restricted Lie superalgebra are given.
We show that there is a family of restricted model filiform Lie superalgebra
$L_{p,p}^{\lambda}$ structures parameterized by elements $\lambda\in
\mathbb{F}^{p}.$ We explicitly describe both the $1$-dimensional ordinary and
restricted cohomology superspaces of $L_{p,p}^{\lambda}$ with coefficients in
the $1$-dimensional trivial module and show that these superspaces are equal.
We also describe the $2$-dimensional ordinary and restricted cohomology
superspaces of $L_{p,p}^{\lambda}$ with coefficients in the $1$-dimensional
trivial module and show that these superspaces are unequal.
