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The impact of stochasticity effects (SEs) in photon emissions on the proton energy spectra during laser-plasma interaction is theoretically investigated in the quantum radiation-dominated regime, which may facilitate SEs experimental observation. We calculate the photon emissions quantum mechanically and the plasma dynamics semiclassically via two-dimensional particle-in-cell simulations. An ultrarelativistic plasma generated and driven by an ultraintense laser pulse head-on collides with another strong laser pulse, which decelerates the electrons due to radiation-reaction effect and results in a significant compression of the proton energy spectra because of the charge separation force. In the considered regime the SEs are demonstrated in the shift of the mean energy of the protons up to hundreds of MeV. This effect is robust with respect to the laser and target parameters and measurable in soon available strong laser facilities.