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Resonant excitation of high-index dielectric nanostructures and their coupling with molecular excitons provide great opportunities for engineering adaptable platforms for hybrid functional optical devices. Here, we numerically calculate resonance coupling of nonradiating anapole states to molecular excitons within silicon nanosphere-J-aggregate heterostructures under illumination with radially polarized cylindrical vector beams. The results show that the resonance coupling is accompanied by a scattering peak around the exciton transition frequency, and the anapole state splits into a pair of anticrossing eigenmodes with a mode splitting energy of ≈200meV. We also investigate the resonance coupling as a function of the J-aggregate parameters, such as thickness, exciton transition linewidth, and oscillator strength. Resonant coupling of the anapole states and J-aggregate heterostructures could be a promising platform for future nanophotonic applications such as in information processing and sensing.