  Suppose $\mathfrak{g}=\mathfrak{g}_{\bar 0}+\mathfrak{g}_{\bar 1} is a Lie
superalgebra of queer type or periplectic type over an algebraically closed
field $\textbf{k}$ of characteristic $p>2$. In this article, we initiate
preliminarily to investigate modular representations of periplectic Lie
superalgebras
  and then verify the first super Kac-Weisfeiler conjecture on the maximal
dimensions of irreducible modules for $\mathfrak{g}$ proposed by the
second-named author in [Shu] where the conjecture is targeted at all
finite-dimensional restricted Lie superalgebras over $\bk$, and already proved
to be true for basic classical Lie superalgebras and completely solvable
restricted Lie superalgebras.
