An exclusive analysis of the four-body final states Λ+p+π++K0 and Σ0+p+π++K0 measured with HADES for p+p collisions at a beam kinetic energy of 3.5 GeV is presented. The analysis uses various phase space variables, such as missing mass and invariant mass distributions, in the four-particle event selection (p,π+,π+,π−) to find cross sections of the different production channels, contributions of the intermediate resonances Δ++ and Σ(1385)+, and corresponding angular distributions. A dominant resonant production is seen, where the reaction Λ+Δ+++K0 has a cross section about ten times higher (29.45±0.08−1.46+1.67±2.06μb) than the analogous nonresonant reaction (2.57±0.02−1.98+0.21±0.18μb). A similar result is obtained in the corresponding Σ0 channels with 9.26±0.05−0.31+1.41±0.65μb in the resonant and 1.35±0.02−1.35+0.10±0.09μb in the nonresonant reactions.