The notions of pseudo-atoms, pseudo-$BCI$ ideals and pseudo-$BCI$ homomorphisms in pseudo-$BCI$ algebras are introduced. Characterizations of a pseudo-$BCI$ ideal are displayed, and conditions for a subset to be a pseudo-$BCI$ ideal are given. The concept of a $\diamond$-medial pseudo-$BCI$ algebra is also introduced, and its characterization is provided. We show that every pseudo-$BCI$ homomorphic image and preimage of a pseudo-$BCI$ ideal is also a pseudo-$BCI$ ideal.