  Using $(1.0087\pm0.0044)\times10^{10}$ $J/\psi$ events collected by the
BESIII detector at the BEPCII collider, we report the first search for the
baryon and lepton number violating decays $\Xi^{0} \rightarrow K^{-} e^{+}$
with $\Delta(B-L)=0$ and $\Xi^{0} \rightarrow K^{+} e^{-}$ with
$|\Delta(B-L)|=2$, where $B$ ($L$) is the baryon (lepton) number. While no
signal is observed, the upper limits on the branching fractions of these two
decays are set to $\mathcal B(\Xi^{0} \rightarrow K^{-}
e^{+})<3.6\times10^{-6}$ and $\mathcal B(\Xi^{0} \rightarrow K^{+}
e^{-})<1.9\times10^{-6}$ at the 90\% confidence level, respectively. These
results offer a direct probe of baryon number violating interactions involving
a strange quark.
