  In this paper, we examine the potentials of the processes $\gamma
\gamma\rightarrow W^{+} W^{-}Z $ and $e^{+}e^{-} \rightarrow e^{+}\gamma^{*}
\gamma^{*} e^{-} \rightarrow e^{+} W^{+} W^{-} Z e^{-}$ at the CLIC with
$\sqrt{s}=0.5,1.5$ and $3$ TeV to investigate anomalous quartic $WWZ\gamma$
couplings by two different CP-violating and CP-conserving effective
Lagrangians. We find $95\%$ confidence level limits on the anomalous coupling
parameters at the three CLIC energies and various integrated luminosities. The
best limits obtained from the process $\gamma \gamma\rightarrow W^{+} W^{-}Z $
on the anomalous $\frac{k_{0}^{W}}{\Lambda^{2}}$,
$\frac{k_{c}^{W}}{\Lambda^{2}}$ and $\frac{k_{2}^{m}}{\Lambda^{2}}$ couplings
defined by CP-conserving effective Lagrangians are $[-1.73;\, 1.73]\times
10^{-7}$ GeV$^{-2}$, $[-2.44;\, 2.44]\times 10^{-7}$ and $[-1.89; \,
1.89]\times 10^{-7}$ GeV$^{-2}$, while $\frac{a_{n}}{\Lambda^{2}}$ coupling
determined by CP-violating effective Lagrangians is obtained as $[-1.74;\,
1.74]\times 10^{-7}$ GeV$^{-2}$. In addition, the best limits derived on
$\frac{k_{0}^{W}}{\Lambda^{2}}$, $\frac{k_{c}^{W}}{\Lambda^{2}}$ and
$\frac{k_{2}^{m}}{\Lambda^{2}}$ and $\frac{a_{n}}{\Lambda^{2}}$ from the
process $e^{+}e^{-} \rightarrow e^{+}\gamma^{*} \gamma^{*} e^{-} \rightarrow
e^{+} W^{+} W^{-} Z e^{-}$ are obtained as $[-1.09;\, 1.09]\times 10^{-6}$
GeV$^{-2}$, $[-1.54;\, 1.54]\times 10^{-6}$ GeV$^{-2}$, $[-1.18;\, 1.18]\times
10^{-6}$ and $[-1.04;\, 1.04]\times 10^{-6}$ GeV$^{-2}$, respectively.
