Singular localization for Quantum groups at generic $q$

We quantize parabolic flag manifolds and describe categories of equivariant quantum $\text{D}$-modules on them at a singular central character. We compute global sections at any $q\in {\text{C}}^{\ast }$ and we also prove a singular version of Beilinson-Bernstein localization for a quantized enveloping algebra $\text{Uq}(\text{g})$, when $q$ is generic.