An exclusive analysis of the four-body final states Λ +p+π^{+}+K^{0} and Σ ^{0}+p+π^{+}+K^{0} 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 \left ( p, π^{+}, π^{+},π^{-} \right ) to find cross sections of the different production channels, contributions of the intermediate resonances Δ ^{++} and Σ \left ( 1385 \right )^{+} , and corresponding angular distributions. A dominant resonant production is seen, where the reaction Λ +Δ ^{++}+K^{0} has a cross section about ten times higher \left ( 29.45± 0.08_{-1.46}^{+1.67}± 2.06 μ b \right ) than the analogous nonresonant reaction \left ( 2.57± 0.02 _{-1.98}^{+0.21}± 0.18μ b \right ). A similar result is obtained in the corresponding Σ ^{0} channels with 9.26± 0.05_{-0.31}^{+1.41}± 0.65 μ b in the resonant and 1.35± 0.02_{-1.35}^{+0.10}± 0.09 μ b in the nonresonant reactions.