The process e+e-→pKS0n̄K-+c.c. and its intermediate processes are studied for the first time, using data samples collected with the BESIII detector at BEPCII at center-of-mass energies of 3.773, 4.008, 4.226, 4.258, 4.358, 4.416, and 4.600 GeV, with a total integrated luminosity of 7.4 fb-1. The Born cross section of e+e-→pKS0n̄K-+c.c. is measured at each center-of-mass energy, but no significant resonant structure in the measured cross-section line shape between 3.773 and 4.600 GeV is observed. No evident structure is detected in the pK-, nKS0, pKS0, nK+, pn̄, or KS0K- invariant mass distributions except for Λ(1520). The Born cross sections of e+e-→Λ(1520)n̄KS0+c.c. and e+e-→Λ(1520)p̄K++c.c. are measured, and the 90% confidence level upper limits on the Born cross sections of e+e-→Λ(1520)Λ̄(1520) are determined at the seven center-of-mass energies. There is an evident difference in line shape and magnitude of the measured cross sections between e+e-→Λ(1520)(→pK-)n̄KS0 and e+e-→pK-Λ̄(1520)(→n̄KS0).