We investigate new physics with light-neutral mediators through coherent elastic neutrino-nucleus scattering ($\mathrm{CE}\nu \mathrm{NS}$) at low energies. These mediators, with a mass of less than 1 GeV, are common properties for extensions of the Standard Model (SM). We consider general scalar, vector, and tensor interactions allowed by Lorentz invariance and involve universal light mediators accordingly. In addition, we study an additional vector gauge boson with an associated $U(1{)}^{\prime }$ gauge group for a variety of models including $U(1{)}_{B-L}$, $U(1{)}_{B-3L_e}$, $U(1{)}_{B-3L_{\mu }}$, and $U(1{)}_{B-3L_{\tau }}$. These models differ in the fermion charges, which determine their contributions within the $\mathrm{CE}\nu \mathrm{NS}$ process. The effects of each model are investigated by embedding them in the SM process using solar neutrino flux. We derive new limits on the coupling-mass plane of these models from the latest CDEX-10 data. We also present projected sensitivities involving the future experimental developments for each model. Our results provide more stringent constraints in some regions, compared to previous works. Furthermore, the projected sensitivities yield an improvement of up to one order of magnitude.

Constraints on couplings of several beyond-Standard-Model-physics scenarios, mediated by massive intermediate particles including (1) an extra Z-prime, (2) a new light spin-1 boson, and (3) a charged Higgs boson, are placed via the neutrino-electron scattering channel to test the Standard Model at a low energy-momentum transfer regime. Data on ${\overline{\nu }}_{\mathrm{e}}-\mathrm{e}$ and ${\nu }_{\mathrm{e}}-\mathrm{e}$ scattering from the TEXONO and LSND, respectively, are used. Upper bounds to coupling constants of the flavor-conserving and flavor-violating new light spin-1 boson and the charged Higgs boson with respect to different mediator masses are determined. The relevant parameter spaces are extended by allowing light mediators. New lower mass limits for extra Z-prime gauge boson models are also placed.