  Compared to other neutrino sources, the huge anti-neutrino fluxes at nuclear
reactor based experiments empower us to derive stronger bounds on non-standard
interactions of neutrinos with electrons mediated by light scalar/vector
mediators. At neutrino energy around $200$~keV reactor anti-neutrino flux is at
least an order of magnitude larger compared to the solar flux. The atomic and
crystal form factors of the detector materials related to the details of the
atomic structure becomes relevant at this energy scale as the momentum
transfers would be small. Non-standard neutrino-electron interaction mediated
by light scalar/vector mediator arises naturally in many low-scale models. We
also propose one such new model with a light scalar mediator. Here, we
investigate the parameter space of such low-scale models in reactor based
neutrino experiments with low threshold Ge and Si detectors, and find the
prospect of probing/ruling out the relevant parameter space by finding the
projected sensitivity at $90 \%$ confidence level by performing a
$\chi^2$-analysis. We find that a detector capable of discriminating between
electron recoil and nuclear recoil signal down to a very low threshold such as
$5$~eV placed in reactor based experiment would be able to probe a larger
region in parameter space compared to the previously explored region. A Ge (Si)
detector with $10$~kg-yr exposure and 1 MW reactor anti-neutrino flux would be
able to probe the scalar and vector mediators with masses below 1 keV for
coupling products $\sqrt{g_\nu g_e}$ $\sim$ $1 \times 10^{-6}~(9.5 \times
10^{-7})$ and $1\times 10^{-7} ~(8\times 10^{-8})$, respectively.
