We present a joint fit of ultra-high-energy cosmic ray (UHECR) source scenarios to data from the Telescope Array (TA) and Pierre Auger Observatory (PAO) experiments [arXiv:2208.12274]. Our simulations account for the propagation of UHECRs through extragalactic space, considering a wide range of source parameters. We fit the spectrum and composition observed by both experiments, taking into account systematic errors. We compare three scenarios to explain the differences in the measured UHECR spectrum above 30 EeV. The first scenario is a systematic scenario with a cosmological homogeneous source distribution and an energy-dependent shift. The second scenario is an astrophysical scenario that combines a cosmological homogeneous source and a local source in the Northern Hemisphere with an energy-independent shift. The third scenario is a combined scenario that includes the presence of a local source, along with an energy-dependent systematic energy shift. Our results indicate that both the astrophysical and systematic scenarios explain the data equally well, while the combined scenario is too complex for the current data. All three scenarios provide similar results for parameters of the cosmological source distribution. We test different mass compositions emitted from the local source and conclude that the data are best described by a source lying at a distance below 26 Mpc that emits cosmic rays dominated by the silicon mass group. In the best-fit astrophysical scenario, the local source lies at a distance of 15 Mpc and emits cosmic rays dominated by the silicon mass group. We discuss other possible parameter combinations and potential source candidates by comparing these results with recent TA anisotropy measurements.