  We perform a detailed combined fit to the $\overline \nu_e \rightarrow
\overline \nu_e$ disappearence data of the Daya Bay experiment and the
appearance $\nu_{\mu} \rightarrow \nu_{e}$ and disappearance $\nu_{\mu}
\rightarrow \nu_{\mu}$ 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 $\oplus$ T2K data
combination constrains the largest radius of the compactified extra dimensions
to be $R\lesssim 0.17$ $\mu {\rm m}$ at 2$\sigma$ 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 charged parity violating phases.
