  In this paper, we explore a canonical connection between the algebra of
$q$-difference operators $\widetilde{V}_{q}$, affine Lie algebra and affine
vertex algebras associated to certain subalgebra $\mathcal{A}$ of the Lie
algebra $\mathfrak{gl}_{\infty}$. We also introduce and study a category
$\mathcal{O}$ of $\widetilde{V}_{q}$-modules. More precisely, we obtain a
realization of $\widetilde{V}_{q}$ as a covariant algebra of the affine Lie
algebra $\widehat{\mathcal{A}^{*}}$, where $\mathcal{A}^{*}$ is a 1-dimensional
central extension of $\mathcal{A}$. We prove that restricted
$\widetilde{V_{q}}$-modules of level $\ell_{12}$ correspond to
$\mathbb{Z}$-equivariant $\phi$-coordinated quasi-modules for the vertex
algebra $V_{\widetilde{\mathcal{A}}}(\ell_{12},0)$, where
$\widetilde{\mathcal{A}}$ is a generalized affine Lie algebra of $\mathcal{A}$.
In the end, we show that objects in the category $\mathcal{O}$ are restricted
$\widetilde{V_{q}}$-modules, and we classify simple modules in the category
$\mathcal{O}$.
