  In this paper, we will analyse three dimensional supersymmetric Yang-Mills
theory coupled to matter fields in $SIM(1)$ superspace formalism. The original
theory which is invariant under the full Lorentz group has $\mathcal{N} =1$
supersymmetry. However, when we break the Lorentz symmetry down to $SIM(1)$
group, the $SIM(1)$ superspace will break half the supersymmetry of the
original theory. Thus, the resultant theory in $SIM(1)$ superspace will have
$\mathcal{N} =1/2$ supersymmetry. This is the first time that $\mathcal{N} =1 $
supersymmetry will be broken down to $\mathcal{N} =1/2$ supersymmetry, for a
three dimensional theory, on a manifold without a boundary. This is because it
is not possible to use non-anticommutativity to break $\mathcal{N} =1$
supersymmetry down to $\mathcal{N} =1/2$ supersymmetry in three dimensions.
