  Motivated by the recent discovery of fractional quantum anomalous Hall states
in moir\'e systems, we consider the possibility of realizing non-Abelian phases
in topological minibands. We study a family of moir\'e systems, skyrmion Chern
band (SCB) models, which can be realized in two-dimensional
semiconductor/magnetic skyrmion heterostructures and also capture the essence
of twisted transition metal dichalcogenide (TMD) homobilayers. We show using
many-body exact diagonalization that, in spite of strong Berry curvature
variations in momentum space, the non-Abelian Moore-Read state can be realized
at half filling of the second miniband. These results demonstrate the
feasibility of non-Abelian fractionalization in moir\'e systems without Landau
levels and shed light on the desirable conditions for their realization. In
particular, we highlight the prospect of realizing the Moore-Read state in
twisted semiconductor bilayers.
