The scattering of a radially polarized (r p) Bessel vortex and nonvortex beam by a perfect electromagnetic conductor (PEMC) sphere is studied based on the generalized Lorenz-Mie theory. The electric and magnetic fields of the incident arbitrary-shaped polarized beams are constructed using vector spherical wave functions (VSWFs) and beam shape coefficients. The analytical expression of the scattered field is expanded using VSWFs and scattering coefficients, which are derived by considering PEMC boundary conditions. The expression of the normalized dimensionless far-field scattering intensity (NDFSI) is also defined and derived. The photonic nanojet (PNJ) and the "bottle beam" generated by the interaction between the PEMC sphere and the vortex and nonvortex Bessel beam under r p are emphasized in this paper. Moreover, the intensity and directivity of NDFSI are also considered. It has been found that the generation of the PNJ and the "bottle beam" is determined by the half-cone angle α 0 of the r p Bessel beam and admittance parameter M of the PEMC sphere. Furthermore, the influence of M, α 0, and integer order l of the Bessel beam on the intensity and distribution of NDFSI is also discussed. The findings are important in the research on meta-materials and promising prospects in microwave engineering, antenna engineering, imaging, subwavelength focusing, optical radiation force, and torque.