  Tunable exciton condensates in two dimensional electron gas systems under
strong magnetic field exhibits anomalous Hall transport owing to mutual Coulomb
coupling, and have attracted a lot of research activity. Here, we explore
another framework using topological flat band models in the absence of Landau
levels, for realizing the many-body exciton phases of two-component fermions
under strong intercomponent interactions. By developing new diagnosis based on
the state-of-the-art density-matrix renormalization group and exact
diagonalization, we show the theoretical discovery of the emergence of Halperin
(111) quantum Hall effect at a total filling factor $\nu=1$ in the lowest Chern
band under strong Hubbard repulsion, which is classified by the unique ground
state with bulk charge insulation and spin superfluidity, The topological
nature is further characterized by one edge branch of chiral propagating
Luttinger modes with level counting $1,1,2,3,5,7$ in consistent with the
conformal field theory description. Moreover, with nearest-neighbor repulsions,
we propose the Halperin (333) fractional quantum Hall effect at a total filling
factor $\nu=1/3$ in the lowest Chern band.
