  Decays of the form $B^{0}_{(s)}\rightarrow J/\psi K_{{\rm S}}^{0} h^+
h^{\left(\prime\right) -}$ ($h^{(\prime)} = K, \pi$) are searched for in
proton-proton collision data corresponding to an integrated luminosity of $1.0
\, {\rm fb}^{-1}$ recorded with the LHCb detector. The first observation of the
$B^{0}_{s}\rightarrow J/\psi K_{{\rm S}}^{0} K^{\pm} \pi^{\mp}$ decay is
reported, with significance in excess of 10 standard deviations. The
$B^{0}\rightarrow J/\psi K_{{\rm S}}^{0} K^{+} K^{-}$ decay is also observed
for the first time. The branching fraction of $B^{0}\rightarrow J/\psi K_{{\rm
S}}^{0} \pi^{+} \pi^{-}$ is determined, to significantly better precision than
previous measurements, using $B^0 \rightarrow J/\psi K_{{\rm S}}^{0}$ as a
normalisation channel. Branching fractions and upper limits of the other
$B^{0}_{(s)}\rightarrow J/\psi K_{{\rm S}}^{0} h^+ h^{\left(\prime\right) -}$
modes are determined relative to that of the $B^{0}\rightarrow J/\psi K_{{\rm
S}}^{0} \pi^{+} \pi^{-}$ decay.
