  Let $k$ be an algebraically closed field of characteristic $l\neq p$. We
construct maximal simple cuspidal $k$-types of Levi subgroups $\mathrm{M}'$ of
$\mathrm{SL}_n(F)$, when $F$ is a non-archimedean locally compact field of
residual characteristic $p$. We show that the supercuspidal support of
irreducible smooth $k$-representations of Levi subgroups $\mathrm{M}'$ of
$\mathrm{SL}_n(F)$ is unique up to $\mathrm{M}'$-conjugation, when $F$ is
either a finite field of characteristic $p$ or a non-archimedean locally
compact field of residual characteristic $p$.
