Considering the fact that the typical three-variable Hindmarsh-Rose(HR) neural model has limitations in describing the complex non-linear features and precise behavior patterns of neuron, the influences of transcranial magneto-acousto-electrical stimulation(TMAES) on firing patterns and resonance effects are analyzed based on an extended HR neural model in this paper. Obtained results show that TMAES can induce transitions in the firing patterns of extended HR neuron, such as spiking and multi-periodic bursting state, etc. If appropriate parameters are selected, the multimodal discharge modes can also be observed. Coefficient of variation is calculated to further investigate the effect of TMAES and Gaussian white noise on the firing rhythm of extended HR neuron, and relevant results indicate that TMAES can induce coherent resonance phenomena in HR neuronal systems similar to the effects of Gaussian white noise, which reveals a new mechanism of coherent resonance induced by TMAES. Further more, TMAES can also regulate coefficient of variation to exhibit anti-coherent resonance and multiple anti-coherent resonance structures, exhibiting richer regulatory functions than Gaussian white noise in regulating neuronal firing rhythm. This study seeks to enhance the understanding of the processes that influence the firing patterns and coherence degree of neuron under TMAES in neuroses or psychoses.