High-frequency oscillations have been frequently observed under the conditions of tearing modes and runaway electrons in J-TEXT Ohmic plasmas. It is found the frequencies of these oscillations range from 20 to 45 kHz, being consistent with the beta-induced Alfvén Eigenmodes (BAEs) with the same order of the low-frequency gap induced by finite beta effects and the coupling of the shear Alfvén wave with the compressional response of the plasma. The exciting conditions for BAEs are investigated, which indicate that runaway electrons, as well as magnetic perturbations contributed by magnetic islands, are indispensable in the excitation of BAEs. In addition, externally applied static resonant magnetic perturbations (RMPs) are used to excite BAEs successfully for the first time in J-TEXT, as indicated by high frequency oscillations (~30 kHz). Further studies show that BAEs can be excited only when the coil current of RMP is stronger than 4 kA, and the strength of BAEs becomes stronger with stronger RMP. To assess the verification of the BAEs, the frequencies of observed modes are compared to the calculated frequencies of the BAE frequency gap in the Alfvén continuum, namely the continuum accumulation point (CAP), and they are found to be close.