Quantum supersymmetric pairs and $\mathrm{ı}$Schur duality of type AIII

We construct quantum supersymmetric pairs $(\mathbf{U},{\mathbf{U}}^{\mathrm{ı}})$ of type AIII and elucidate their fundamental properties. An $\mathrm{ı}$Schur duality between the $\mathrm{ı}$quantum supergroup ${\mathbf{U}}^{\mathrm{ı}}$ and the Hecke algebra of type B acting on a tensor space is established, providing a super generalization of the $\mathrm{ı}$Schur duality of type AIII. Additionally, we construct a (quasi) $K$-matrix for arbitrary parameters, which facilitates the realization of the Hecke algebra action on the tensor space.