Invariant theory of $\mathrm{ı}$quantum groups of type AIII

We develop an invariant theory of quasi-split $\mathrm{ı}$quantum groups ${\mathbf{U}}_n^{\mathrm{ı}}$ of type AIII on a tensor space associated to $\mathrm{ı}$Howe dualities. The first and second fundamental theorems for ${\mathbf{U}}_n^{\mathrm{ı}}$-invariants are derived.