  We study fermions on a triangular lattice model that exhibits topological
flatbands characterized by nonzero Chern numbers. Our scheme stems from the
well-known Hofstadter model but the next-nearest-neighbor hopping is
introduced, which is crucial for tuning the lowest band to be nearly flat.
Differing from previous proposals with the necessity of multiparticle
interactions, we consider the more realistic long-range dipolar interaction
combined with two-body short-range attractions between fermions. We show the
realization of the non-Abelian $\nu=1/2$ Moore-Read fractional Chern
insulators, and strong evidence for the existence of the more exotic $\nu=3/5$
Read-Rezayi fractional Chern insulators. Our results provide insights for the
experimental realization of these exotic states by realistic two-body
interactions and thus facilitates the implementation of the universal
topological quantum computation.
