  We study D3 branes at orbifolded conifold singularities in the presence of
discrete torsion. The vacuum moduli space of open strings becomes
non-commutative due to a deformation of the superpotential and is studied via
the representation theory of the moduli algebra. It is also shown that the
center of the moduli algebra correctly describes the underlying orbifolded
conifolds. The field theory can be obtained by a marginal deformation of the
${\cal N} = 1$ gauge theory on D3 branes at conifold singularity, the global
symmetry being broken from $SU(2) \times SU(2)$ to $U(1) \times U(1)$. By using
the AdS/CFT correspondence we argue that the marginal deformation is related to
massless KK modes of NSNS and RR two form reduced on the compact space
$T^{1,1}$. We build a $T^2$ fibration of $T^{1,1}$ and show that a D3 brane in
the bulk correspond to a D5 brane on the $T^2$ fibre. We also discuss the
possible brane construction of the system.
