  We investigate electronic states in a two-dimensional network consisting of
interacting quantum wires, a model adopted for twisted bilayer systems. We
construct general operators which describe various scattering processes in the
system. In a twisted bilayer structure, the moir\'e periodicity allows for
generalized umklapp scatterings, leading to a class of correlated states at
certain fractional fillings. We identify scattering processes which can lead to
an insulating gapped bulk with gapless chiral edge modes at fractional
fillings, resembling the quantum anomalous Hall effect recently observed in
twisted bilayer graphene. Finally, we demonstrate that the description can be
useful in predicting spectroscopic and transport features to detect and
characterize the chiral edge modes in the moir\'e-induced correlated states.
