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We have estimated the sensitivity to the anomalous couplings of the$\gamma\gamma\gamma Z$ vertex in the $\gamma\gamma\rightarrow\gamma Z$scattering of the Compton backscattered photons at the CLIC. Both polarized andunpolarized collisions at the $e^+e^-$ energies 1500 GeV and 3000 GeV areaddressed, and anomalous contributions to helicity amplitudes are derived. Thedifferential and total cross sections are calculated. We have obtained 95\%C.L. exclusion limits on the anomalous quartic gauge couplings (QGCs). They arecompared with corresponding bounds derived for the $\gamma\gamma\gamma Z$couplings via $\gamma Z$ production at the LHC. The constraints on theanomalous QGCs are one to two orders of magnitude more stringent that at theHL-LHC. The partial-wave unitarity constraints on the anomalous couplings areexamined. It is shown that the unitarity is not violated in the region of theanomalous QGCs studied in the paper.

Probing anomalous $\gamma\gamma\gamma Z$ couplings through $\gamma Z$ production in $\gamma\gamma$ collisions at the CLIC