Optomagnonic structures are widely studied in the field of nanophotonics and quantum information science. They are the key platforms for the realization of magnon-mediated microwave to optical transducers in various applications of quantum computing. In order to enhance the coupling between light (photons) and spin waves (magnons), here in this work, we use the Lagrange multiplication method to find the optimum matching condition between the optical whispering-gallery mode and the magnon with Kittle and higher-order modes in microresonators. It is found that the magnon modes located near the edge of the resonator exhibits stronger coupling strength with the optical modes. Numerically, we find the coupling constant can approach 87.6×2π H z in Kittle mode, and 459×2π H z in high-order magnon mode for a yttrium iron garnet (YIG, Y3Fe5O12 ) microdisk cavity with a radius of 300 microns and a thickness of 10 microns. We believe these results may provide an efficient way for enhancing the magneto-optical interaction in the optical devices, which will facilitate the development of magneto-optical control, optical-microwave interaction, and optical nonlinearity.