Atmospheric pressure plasma jet has received widespread attention due to its enormous potential applications in various fields, and its discharge conditions play a key role in changing their physical and chemical properties and ultimately determining its application effectiveness. Factors such as discharge voltage, gas flow rate, and the introduction of an external magnetic field intricately influence the performance of plasma jet. The combined effects of any two of these factors can yield enhanced outcomes, while also bringing complexity to the discharge phenomenon. However, there is currently a lack of research on the combined effects of external magnetic field, discharge voltage, and gas flow rate on the characteristics of plasma jets, making it difficult to comprehensively evaluate the discharge characteristics of plasma jet under multiple discharge conditions. Therefore, this paper focuses on an AC excited atmospheric pressure argon plasma jet and investigates the combined effects of external magnetic field, discharge voltage, and gas flow rate on various characteristic parameters of the plasma jet, including macroscopic morphology, discharge power, gas temperature T_g, electron excitation temperature T_exc, electron density n_e, emission intensity of excited state Ar* particles, and number density of ground state ·OH particles by using methods of camera shooting, and electrical parameter measurement, spectroscopic analysis of emission and absorption spectra. The obtained results are shown below. The effect of discharge voltage on the characteristic parameters of the plasma jet is not affected by gas flow rate or the existence of an external magnetic field. The increase of discharge voltage can improve jet performance by enhancing the discharge power, extending the plasma plume length, elevating the gas temperature T_g and electron excitation temperature T_exc, increasing the electron density n_e and emission intensity of excited state Ar* particles, as well as the number density of ground state ·OH particles. The addition of an external magnetic field can improve the jet performance without significantly changing the discharge power, and the extent of this improvement is influenced by the mode of magnetic field action. Notably, the enhancement of jet performance is most significant when the magnetic field selectively targets the plasma plume, excluding direct interaction with electrode discharge region. The effect of gas flow rate on jet performance becomes intricate: it is intertwined with the effect of voltage and the effect of external magnetic field. When an external magnetic field is present, excessive voltage and gas flow rate may reduce the number density of ground state ·OH particles generated by plasma jet. This underscores the need for a detailed understanding when optimizing jet performance under various discharge conditions. Simply combining the optimal conditions for each individual factor does not guarantee the achievement of peak jet performance when all three discharge conditions work synergistically. This study presents valuable insights into the discharge characteristics of plasma jet under different discharge conditions, providing guidance for optimizing the performance of plasma jet and promoting the advancement of atmospheric pressure plasma jet technology in different application fields.