  We generalize the mathematical definition of Coulomb branches of
$3$-dimensional $\mathcal N=4$ SUSY quiver gauge theories in arXiv:1503.03676,
arXiv:1601.03686, arXiv:1604.03625 to the cases with symmetrizers. We obtain
generalized affine Grassmannian slices of type $BCFG$ as examples of the
construction, and their deformation quantizations via truncated shifted
Yangians. Finally, we study modules over these quantizations and relate them to
the lower triangular part of the quantized enveloping algebra of type $ADE$.
