  Recent discoveries of zero-field fractional Chern insulators in moir\'e
materials have attracted intensive research interests. However, most current
theoretical and experimental attempts focus on systems with low Chern number
bands, in analogy to the Landau levels. Here we propose candidate material
systems for realizing fractional Chern insulators with higher Chern numbers.
The material setup involves $\Gamma$-valley twisted homobilayer transition
metal dichalcogenides in proximity to a skyrmion lattice. The skyrmion exchange
potential induces a flat band with a high Chern number $C = -2$. Using the
momentum-space projected exact diagonalization method, we perform a
comprehensive study at various filling factors, confirming the generalized Jain
series. Our research provides theoretical guidance on realizing unconventional
fractional Chern insulators beyond the Landau level picture.
