The properties of atmospheric pressure collisional plasma sheath with non-extensively distributed electrons and hypothetical ionization source terms are studied in this work. The Bohm criterion for the magnetized plasma was extended in the presence of an ion-neutral collisional force and ionization source. The effects of electron non-extensive distribution, ionization frequency, ionneutral collision, magnetic field angle and ion temperature on the Bohm criterion of the plasma sheath are numerically analyzed. The fluid equations are solved numerically in the plasma-wall transition region using a modified Bohm criterion as the boundary condition. The plasma sheath properties such as charged particle density, floating sheath potential and thickness are thoroughly investigated under different kinds of ion source terms, the contributions of collisions, and magnetic fields. The results show that the effect of the ion source term on the properties of atmospheric pressure collisional plasma sheath is significant. As the ionization frequency increases, the Mach number of Bohm criterion decreases and the range of possible values narrows. When the ion source is considered, the space charge density increases, the sheath potential drops more rapidly, and the sheath thickness becomes narrower. In addition, ion-neutral collision, magnetic field angle and ion temperature also significantly affect the sheath potential profile and sheath thickness.