AbstractThe anomalous quartic neutral couplings of the$$\gamma \gamma \gamma \gamma $$γγγγvertex in a polarized light-by-light scattering of the Compton backscattered photons at the CLIC are examined. Both differential and total cross sections are calculated for$$e^+e^-$$e+e-collision energies 1500 GeV and 3000 GeV. The helicity of the initial electron beams is taken to be$$\pm \,0.8$$±0.8. The unpolarized and SM cross sections for the same values of helicities are also estimated. The 95% C.L. exclusion limits on two anomalous photon couplings$$\zeta _1$$ζ1and$$\zeta _2$$ζ2are calculated. The best bounds on these couplings are found to be$$6.85 \times 10^{-16} \text { GeV}^{-4}$$6.85×10-16GeV-4and$$1.43 \times 10^{-15} \text { GeV}^{-4}$$1.43×10-15GeV-4, respectively. The results are compared with the exclusion bounds obtained previously for the LHC and HL-LHC. It is shown that the light-by-light scattering at the CLIC, especially the polarized, has a greater potential to search for the anomalous quartic neutral couplings of the$$\gamma \gamma \gamma \gamma $$γγγγvertex.