The photoproduction of bottomonium-like states $Z_{b}(10610)$ and $Z_{b}(10650)$ via $gamma p$ scattering is studied within an effectiv Lagrangian approach and the vector-meson-dominance model. The Regge model is employed to calculate the photoproduction of $Z_{b}$ states via $t$-channel with $pi$ exchange.The numerical results show that the values of the total cross-sections of $Z_{b}(10610)$ and $Z_{b}(10650)$ can reach 0.09 nb and 0.02 nb, respectively, near the center of mass energy of 22 GeV. The experimental measurements and studies on the photoproduction of $Z_{b}$ states near energy region around $Wsimeq 22$ GeV is suggested. Moreover, with the help of eSTARlight and STARlight programs, one obtains the cross-sections and event numbers of $Z_{b}(10610)$ production in electron-ion collision (EIC) and Ultraperipheral collisions (UPCs). The results show that a considerable number of events from $Z_{b}(10610)$ can be produced on the relevant experiments of EICs and UPCs. Also, one calculates the rates and kinematic distributions for $gamma prightarrow Z_{b}n$ in $ep$ and $pA$ collisions via EICs and UPCs, and the relevant results will provide an important reference for the RHIC, LHC, EIC-US, LHeC, and FCC experiments to search for the bottomonium-like $Z_{b}$ states.
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