In this paper, we investigated the characteristics of a magnetized plasma sheath, which contains positive ions, electrons and neutral particles. In the model used, the distribution of electrons is assumed to follow Tsallis non-extensive statistics, and the ions are treated as a fluid using the continuity and momentum transfer equations, taking into account the ion source term. Using the Sagdeev potential method, we established the modified Bohm sheath criterion to obtain the required velocity of ions at the sheath entrance. To solve the model equations in the plasma sheath region, we used the Runge–Kutta fourth-order method. Furthermore, we examined the impact of the ionization frequency and the magnetic field angle on the sheath characteristics, such as the electron and ion densities, the electric potential and the ion velocity. The results show a considerable influence of ionization frequency and magnetic field angle on the behavior of plasma sheath characteristics. Additionally, it is demonstrated that the ion source term makes the impact of the magnetic field angle more significant. This study may be useful for enhancing and advancing techniques in plasma-assisted surface treatment, particularly in microelectronic applications, semiconductor industry and fusion energy studies.