  The production of heavy-flavored hadron at the hadronic colliders provides a
challenging opportunity to test the validity of pQCD predictions. There are two
mechanisms for the $B^{(*)}_s$ hadroproduction, i.e. the gluon-gluon fusion
mechanism via the subprocess $g+g\rightarrow B^{(*)}_s+b+\bar{s}$ and the
extrinsic heavy quark mechanism via the subprocesses $g+\bar{b}\to B^{(*)}_s
+\bar{s}$ and $g+s\to B^{(*)}_s +b$, both of which shall have sizable
contributions in proper kinematic region. Different from the
fixed-flavor-number scheme (FFNS) previously adopted in the literature, we
study the $B^{(*)}_s$ hadroproduction under the general-mass
variable-flavor-number scheme (GM-VFNS), in which we can consistently deal with
the double counting problem from the above two mechanisms. Properties for the
$B^{(*)}_s$ hadroproduction are discussed. To be useful reference, a
comparative study of FFNS and GM-VFNS is presented. Both of which can provide
reasonable estimations for the $B^{(*)}_s$ hadroproduction. At the Tevatron,
the difference between these two schemes is small, however such difference is
obvious at the LHC. The forthcoming more precise data on LHC shall provide a
good chance to check which scheme is more appropriate to deal with the
$B^{(*)}_s$-meson production and to further study the heavy quark components in
hadrons.
