  We investigate magneto-transport properties of a $\theta$ shaped three-arm
mesoscopic ring where the upper and lower sub-rings are threaded by
Aharonov-Bohm fluxes $\phi_1$ and $\phi_2$, respectively, within a
non-interacting electron picture. A discrete lattice model is used to describe
the quantum network in which two outer arms are subjected to binary alloy
lattices while the middle arm contains identical atomic sites. It is observed
that the presence of the middle arm provides localized states within the band
of extended regions and lead to the possibility of switching action from a high
conducting state to a low conducting one and vice versa. This behavior is
justified by studying persistent current in the network. Both the total current
and individual currents in three separate branches are computed by using
second-quantized formalism and our idea can be utilized to study magnetic
response in any complicated quantum network. The nature of localized
eigenstates are also investigated from probability amplitudes at different
sites of the quantum device.
