  We investigate coherent-elastic neutrino-nucleus scattering ($CE\nu NS$) in
3-3-1 models for different values of $\beta$ in which $\beta$ is a parameter
used to define the charge operator of the 331 models. We show that the number
of events predicted by 331$\beta$ model is in agreement with the data given by
COHERENT experiment. We evaluate the sensitivity of the mass of Z' boson with
90% confidence level (CL) and find that $m_{Z'}\geq 1.4 $TeV for
$\beta=-\sqrt{3}$ with 90% CL. We perform $\chi^2$ fit for liquid Argon,
Germanium and NaI detector subsystems, we obtain $m_{Z'} \geq [2,3.1 ]$ TeV
with 90\% CL. Our results indicate low-energy high-intensity measurements can
provide a valuable probe, complementary to high energy collider searches at LHC
and electroweak precision measurements.
