We introduce a unique type of partially coherent light (PCL) that simultaneously carries a vortex phase and exhibits a special spatial correlation structure, known as radially polarized multi-Gaussian Schell-model fractional vortex (RP-MGSM-FV) beams. We outline the fundamental requirements for generating such light beams and derive the analytical expression for their cross-spectral density matrix after transmission through ABCD optical systems. We further examine the influence of the topological charge magnitude, sign, and coherence width of its vortex phase component on the intensity distribution at the focal plane. The results indicate that as the coherence width increases, the intensity distribution at the focal plane translates from a flat-top to a Gaussian-like shape, then to a flat-top, and ultimately to a ring pattern. An increase in the topological charge numbers leads to a distinct separation in the spatial distribution of the beam at the focal plane. Additionally, changes in the sign of the topological charge cause an inversion in the spatial distribution pattern, allowing for the detection of both the magnitude and sign of the topological charge in RP-MGSM-FV beams. These findings are significantly valuable in applications such as free-space optical communications and particle trapping in micro domains.