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We investigate an experimental toy-model system of a pseudospin-half square-lattice Hubbard Hamiltonian in [(SrIrO_{3})_{1}/(CaTiO_{3})_{1}] to include both nontrivial complex hopping and moderate electron correlation. While the former induces electronic Berry phases as anticipated from the weak-coupling limit, the latter stabilizes an antiferromagnetic Mott insulator ground state analogous to the strong-coupling limit. Their combined results in the real system are found to be an anomalous Hall effect with a nonmonotonic temperature dependence due to the competition of the antiferromagnetic order and charge excitations in the Mott state, and an exceptionally large Ising anisotropy that is captured as a giant magnon gap beyond the superexchange approach. The unusual phenomena highlight the rich interplay of electronic topology and electron correlation in the intermediate-coupling regime that is largely unexplored and challenging in theoretical modeling.