The two-channel photoproductions of $gamma p to K^{*+} Sigma^{0}$ and $gamma p to K^{*0} Sigma^{+}$ are investigated based on an effective Lagrangian approach at the tree-level Born approximation. In addition to the $t$-channel $K$, $kappa$, $K^*$ exchanges, the $s$-channel nucleon ($N$) and $Delta$ exchanges, the $u$-channel $Lambda$, $Sigma$, $Sigma^*$ exchanges, and the generalized contact term, we try to take into account the minimum number of baryon resonances in constructing the reaction amplitudes to describe the experimental data. It is found that by including the $Delta(1905)5/2^+$ resonance with its mass, width, and helicity amplitudes taken from the Review of Particle Physics [Particle Data Group, C. Patrignani {it et al.}, Chin. Phys. C {bf 40}, 100001 (2016)], the calculated differential and total cross sections for these two reactions are in good agreement with the experimental data. An analysis of the reaction mechanisms shows that the cross sections of $gamma p to K^{*+}Sigma^{0}$ are dominated by the $s$-channel $Delta(1905)5/2^+$ exchange at low energies and $t$-channel $K^*$ exchange at high energies, with the $s$-channel $Delta$ exchange providing significant contributions in the near-threshold region. For $gamma p to K^{*0}Sigma^{+}$, the angular dependences are dominated by the $t$-channel $K$ exchange at forward angles and the $u$-channel $Sigma^*$ exchange at backward angles, with the $s$-channel $Delta$ and $Delta(1905)5/2^+$ exchanges making considerable contributions at low energies. Predictions are given for the beam, target, and recoil asymmetries for both reactions.
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