  We study macroscopically two dimensional $\mathcal{N}=(2,2)$ supersymmetric
gauge theories constructed by compactifying the quiver gauge theories with
eight supercharges on a product $\mathbb{T}^{d} \times
\mathbb{R}^{2}_{\epsilon}$ of a $d$-dimensional torus and a two dimensional
cigar with $\Omega$-deformation. We compute the universal part of the effective
twisted superpotential. In doing so we establish the correspondence between the
gauge theories, quantization of the moduli spaces of instantons on
$\mathbb{R}^{2-d} \times \mathbb{T}^{2+d}$ and singular monopoles on
$\mathbb{R}^{2-d} \times \mathbb{T}^{1+d}$, for $d=0,1,2$, and the Yangian
$\mathbf{Y}_{\epsilon}(\mathfrak{g}_{\Gamma})$, quantum affine algebra
$\mathbf{U}^{\mathrm{aff}}_q(\mathfrak{g}_{\Gamma})$, or the quantum elliptic
algebra $\mathbf{U}^{\mathrm{ell}}_{q,p}(\mathfrak{g}_{\Gamma})$ associated to
Kac-Moody algebra $\mathfrak{g}_{\Gamma}$ for quiver $\Gamma$.
