  In this paper, we study basic properties of global $\jmath$-crystal bases for
integrable modules over a quantum symmetric pair coideal subalgebra
$\mathbf{U}^{\jmath}$ associated to the Satake diagram of type AIII with even
white nodes and no black nodes. Also, we obtain an intrinsic characterization
of the $\jmath$-crystal bases, whose original definition is artificial.
