  In this paper, we present a canonical quantization of Lie bialgebra
structures on the formal power series $\mathfrak{d}[\![t]\!]$ with coefficients
in the cotangent Lie algebra $\mathfrak{d} = T^*\mathfrak{g} = \mathfrak{g}
\ltimes \mathfrak{g}^*$ to a simple complex Lie algebra $\mathfrak{g}$. We
prove that these quantizations produce twists to the natural analog of the
Yangian for $\mathfrak{d}$. Moreover, we construct spectral $R$-matrices for
these twisted Yangians as compositions of twisting matrices.
  The motivation for the construction of these twisted Yangians over
$\mathfrak{d}$ comes from certain 4d holomorphic-topological gauge theory. More
precisely, we show that pertubative line operators in this theory can be
realized as representations of these Yangians. Moreover, the comultiplications
of these Yangians correspond to the monodial structure of the category of line
operators.
