The measurements of coherent elastic neutrino-nucleus scattering (CEνNS) experiments have opened up the possibility to constrain neutrino physics beyond the standard model of elementary particle physics. Furthermore, by considering neutrino-electron scattering in the keV-energy region, it is possible to set additional limits on new physics processes. Here, we present constraints that are derived from Conus germanium data on beyond the standard model (BSM) processes like tensor and vector non-standard interactions (NSIs) in the neutrino-quark sector, as well as light vector and scalar mediators. Thanks to the realized low background levels in the Conus experiment at ionization energies below 1 keV, we are able to set the world’s best limits on tensor NSIs from CEνNS and constrain the scale of corresponding new physics to lie above 360 GeV. For vector NSIs, the derived limits strongly depend on the assumed ionization quenching factor within the detector material, since small quenching factors largely suppress potential signals for both, the expected standard model CEνNS process and the vector NSIs. Furthermore, competitive limits on scalar and vector mediators are obtained from the CEνNS channel at reactor-site which allow to probe coupling constants as low as 5 ∙ 10−5 of low mediator masses, assuming the currently favored quenching factor regime. The consideration of neutrino-electron scatterings allows to set even stronger constraints for mediator masses below ∼ 1 MeV and ∼ 10 MeV for scalar and vector mediators, respectively.