  Models of neutrino mixing involving one or more sterile neutrinos have
resurrected their importance in the light of recent cosmological data. In this
case, reactor antineutrino experiments offer an ideal place to look for
signatures of sterile neutrinos due to their impact on neutrino flavor
transitions. In this work, we show that the high-precision data of the Daya Bay
experi\-ment constrain the 3+1 neutrino scenario imposing upper bounds on the
relevant active-sterile mixing angle $\sin^2 2 \theta_{14} \lesssim 0.06$ at
3$\sigma$ confidence level for the mass-squared difference $\Delta m^2_{41}$ in
the range $(10^{-3},10^{-1}) \, {\rm eV^2}$. The latter bound can be improved
by six years of running of the JUNO experiment, $\sin^22\theta_{14} \lesssim
0.016$, although in the smaller mass range $ \Delta m^2_{41} \in (10^{-4}
,10^{-3}) \, {\rm eV}^2$. We have also investigated the impact of sterile
neutrinos on precision measurements of the standard neutrino oscillation
parameters $\theta_{13}$ and $\Delta m^2_{31}$ (at Daya Bay and JUNO),
$\theta_{12}$ and $\Delta m^2_{21}$ (at JUNO), and most importantly, the
neutrino mass hierarchy (at JUNO). We find that, except for the obvious
situation where $\Delta m^2_{41}\sim \Delta m^2_{31}$, sterile states do not
affect these measurements substantially.
