  In this article we consider the presence of neutrino non-standard
interactions (NSI) in the production and detection processes of reactor
antineutrinos at the Daya Bay experiment. We report for the first time, the new
constraints on the flavor non-universal and flavor universal charged-current
NSI parameters, estimated using the currently released 621 days of Daya Bay
data. New limits are placed assuming that the new physics effects are just
inverse of each other in the production and detection processes. With this
special choice of the NSI parameters, we observe a shift in the oscillation
amplitude without distorting the $L/E$ pattern of the oscillation probability.
This shift in the depth of the oscillation dip can be caused by the NSI
parameters as well as by $\theta_{13}$, making it quite difficult to
disentangle the NSI effects from the standard oscillations. We explore the
correlations between the NSI parameters and $\theta_{13}$ that may lead to
significant deviations in the reported value of the reactor mixing angle with
the help of iso-probability surface plots. Finally, we present the limits on
electron, muon/tau, and flavor universal (FU) NSI couplings with and without
considering the uncertainty in the normalization of the total event rates.
Assuming a perfect knowledge of the event rates normalization, we find strong
upper bounds $\sim$ 0.1\% for the electron and FU cases improving the present
limits by one order of magnitude. However, for a conservative error of 5\% in
the total normalization, these constraints are relaxed by almost one order of
magnitude.
