  Motivated by the recent discovery of a charmonium $X(3960)$ in $B$ decays by
the LHCb Collaboration, the likely existence of two bound/virtual states
(denoted by $ X_{s\bar{s}}$ and $ X_{q\bar{q}}$) below the $D_{s}^{+}D_{s}^{-}$
and $\bar{D}D$ mass thresholds has been re-examined recently. In this work, we
employ the effective Lagrangian approach to calculate their production rates in
$B$ decays utilizing triangle diagrams. Our results show that the production
yields of $B^{+}\to X_{s\bar{s}} K^{+}$ and $B^{+}\to X_{q\bar{q}} K^{+}$ are
of the order of $10^{-4}$, in agreement with the relevant experimental data,
which indicates that, if the $D_{s}^{+}D_{s}^{-}$ and $\bar{D}D$ bound states
indeed exist, they can be detected in $B$ decays. Moreover, we calculate the
production rate of $B^{+}\to X(3960) K^{+}$ assuming that $X(3960)$ is a
resonant state of $D_{s}^{+}D_{s}^{-}$ and find that it is also of the order of
$10^{-4}$ but a bit smaller than that as a $D_s^+D_s^-$ bound state.

High Energy Physics - Phenomenology