  Dark matter (DM) direct detection experiments are entering the multiple-ton
era and will be sensitive to the coherent elastic neutrino nucleus scattering
(CE$\nu$NS) of solar neutrinos, enabling the possibility to explore
contributions from new physics with light mediators at the low energy range. In
this paper we consider light mediator models (scalar, vector and axial vector)
and the corresponding contributions to the solar neutrino CE$\nu$NS process.
Motivated by the current status of new generation of DM direct detection
experiments and the future plan, we study the sensitivity of light mediators in
DM direct detection experiments of different nuclear targets and detector
techniques. The constraints from the latest $^8$B solar neutrino measurements
of XENON-1T are also derived. Finally, We show that the solar neutrino
CE$\nu$NS process can provide stringent limitation on the $ L_{\mu}-L_{\tau} $
model with the vector mediator mass below 100 MeV, covering the viable
parameter space of the solution to the $ (g-2)_{\mu}$ anomaly.
