  In this paper, we will study the deformation of a three dimensional
$\mathcal{N} = 2$ supersymmetry gauge theory. We will deform this theory by
imposing non-anticommutativity. This will break the supersymmetry of the theory
from $\mathcal{N} = 2$ supersymmetry to $\mathcal{N} = 1$ supersymmetry. We
will address the problem that occurs in the Landau gauge due to the existence
of multiple solutions to the gauge fixing condition. This will be done by
generalizing the Faddeev-Popov method. This formalism is motivated from the
Nicolai map in topological field theories. Finally, we will study the extended
BRST symmetry that occurs in this theory.
