Let $G$ be a complex reductive group and $\mathbf N$ its finite dimensional representation (possibly zero). The quantized Coulomb branch is defined (with Braverman, Finkelberg) as the equivariant (K-)homology of a certain space $\mathcal R_{G,\mathbf N}$, which is analog of the affine Steinberg variety. Thus quantized Coulomb branches are analog of DAHA, which are the equivariant K-theory of the affine Steinberg variety by Vasserot and Varagnolo-Vasserot. We will study modules of quantized Coulomb branches by applying their techniques used for modules of DAHA.