  We explore a $Z_{2}$ fractionalized Bardeen-Cooper-Schrieffer (BCS)
superconducting state, which is a minimal extension of usual BCS framework. It
is found that this state has similar thermal and transport properties, but its
single-particle feature strongly deviates from the coherent quasiparticle
behavior of the classic/conventional BCS superconducting state. The fingerprint
of such $Z_{2}$ BCS state is the absence of the BCS coherent peaks and instead
a kink in the local density of state occurs, which in principle could be probed
by scanning tunneling microscopy or point-contact spectroscopy experiments. The
corresponding exactly soluble models that realize the desirable $Z_{2}$
fractionalized BCS state is presented. In addition, we also study the extended
$t$-$U$-$J$ model by using $Z_{2}$ slave-spin representation and find that the
$Z_{2}$ BCS state may exist when the paring structure is fully gapped or has
nodes. The prototypical wave-function of such a $Z_{2}$ BCS state is also
proposed, which could be taken as trial wave-function in current numerical
techniques. The present work may be helpful to further study the unconventional
superconductivity and its relation to non-Fermi liquids.
