  We develop a strong coupling approach towards quantum magnetism in Mott
insulators for Wannier obstructed bands. Despite the lack of Wannier orbitals,
electrons can still singly occupy a set of exponentially-localized but
nonorthogonal orbitals to minimize the repulsive interaction energy. We develop
a systematic method to establish an effective spin model from the electron
Hamiltonian using a diagrammatic approach. The nonorthogonality of the Mott
basis gives rise to multiple new channels of spin-exchange (or permutation)
interactions beyond Hartree-Fock and superexchange terms. We apply this
approach to a Kagome lattice model of interacting electrons in Wannier
obstructed bands (including both Chern bands and fragile topological bands).
Due to the orbital nonorthogonality, as parameterized by the nearest neighbor
orbital overlap $g$, this model exhibits stable ferromagnetism up to a finite
bandwidth $W\sim U g$, where $U$ is the interaction strength. This provides an
explanation for the experimentally observed robust ferromagnetism in Wannier
obstructed bands. The effective spin model constructed through our approach
also opens up the possibility for frustrated quantum magnetism around the
ferromagnet-antiferromagnet crossover in Wannier obstructed bands.
