  Recent experimental discovery of fractional Chern insulator in moir\'e Chern
band in twisted transition metal dichalocogenide homobilayers has sparked
intensive interest in exploring the ways of engineering band topology and
correlated states in moir\'e systems. In this letter, we demonstrate that, with
an additional exchange interaction induced by proximity effect, the topology
and bandwidth of the moir\'e minibands of twisted $\mathrm{MoTe_2}$
homobilayers can be easily tuned. Fractional Chern insulators at -2/3 filling
are found to appear at enlarged twist angles over a large range of twist angles
with enhanced many-body gaps. We further discover a topological phase
transition between the fractional Chern insulator, quantum anomalous Hall
crystal, and charge density wave. Our results shed light on the interplay
between topology and correlation physics.
