  For the first time, we estimate the in-medium mass shift of the two-flavored
heavy mesons $B_c, B_c^*, B_s, B_s^*, D_s$ and $D_s^*$ in symmetric nuclear
matter. The estimates are made by evaluating the lowest order one-loop
self-energies. The enhanced excitations of intermediate state heavy-light
mesons in symmetric nuclear matter are the origin of their negative mass shift.
Our results show that the magnitude of the mass shift for the $B_c$ meson
($\bar{b} c$ or $b \bar{c}$) is larger than those of the $\eta_c (\bar{c} c)$
and $\eta_b (\bar{b} b)$, different from a naive expectation that it would be
in-between of them. While, that of the $B_c^*$ shows the in-between of the
$J/\psi$ and $\Upsilon$. We observe that the lighter vector meson excitation in
each meson self-energy gives a dominant contribution for the corresponding
meson mass shift, $B_c, B_s,$ and $D_s$.
