  We provide a combinatorial characterization of two-sided cells in modified
$\imath$quantum groups of type AIII. Our approach is to lift a corresponding
description of two-sided cells in $\jmath$-Schur algebras associated to
Iwahori--Hecke algebras of type $B$. We further give a combinatorial
description of two-sided cells in other two kinds of Schur-type algebras,
namely $\imath$-Schur algebras and $\tilde{\imath}$-Schur algebras.
