[en] We perform a detailed combined fit to the ${\stackrel{¯<!--\; ??\; -->}{\mathrm{\nu <!--\; ??\; -->}}}_e\to <!--\; ???\; -->{\stackrel{¯<!--\; ??\; -->}{\mathrm{\nu <!--\; ??\; -->}}}_e$ disappearence data of the Daya Bay experiment and the appearance ${\mathrm{\nu <!--\; ??\; -->}}_{\mathrm{\mu <!--\; ??\; -->}}\to <!--\; ???\; -->{\mathrm{\nu <!--\; ??\; -->}}_e$ and disappearance ${\mathrm{\nu <!--\; ??\; -->}}_{\mathrm{\mu <!--\; ??\; -->}}\to <!--\; ???\; -->{\mathrm{\nu <!--\; ??\; -->}}_{\mathrm{\mu <!--\; ??\; -->}}$ data of the Tokai to Kamioka (T2K) one in the presence of two models of new physics affecting neutrino oscillations, namely a model where sterile neutrinos can propagate in a large compactified extra dimension and a model where non-standard interactions (NSI) affect the neutrino production and detection. We find that the Daya Bay ⨁ T2K data combination constrains the largest radius of the compactified extra dimensions to be $R\lesssim <!--\; ???\; -->0.17$ μm at 2σ C.L. (for the inverted ordering of the neutrino mass spectrum) and the relevant NSI parameters in the range $\mathcal{O}({10}^{-<!--\; ???\; -->3})-<!--\; ???\; -->\mathcal{O}({10}^{-<!--\; ???\; -->2})$, for particular choices of the charge parity violating phases. (paper)