  Two near-threshold peaking structures with spin-parities $J^{\mathrm{PC}
}=0^{++}$ were recently discovered by the LHCb Collaboration in the $
D_{s}^{+}D_{s}^{-}$ invariant mass distribution of the decay $ B^{+}\rightarrow
D_{s}^{+}D_{s}^{-}K^{+}$. The first of them is the resonance $X(3960)$, whereas
the second one, $X_0(4140)$, is a structure with the mass around
$4140~\mathrm{MeV}$. To explore their natures and model them, we study the
hadronic molecule $\mathcal{M}=D_s^{+}D_s^{-}$ and calculate its mass, current
coupling, and width. The mass and current coupling of the molecule are
extracted from the QCD two-point sum rule analyses by taking into account
vacuum condensates up to dimension $10$. To evaluate its full width, we
consider the processes $\mathcal{M} \to D_{s}^{+}D_{s}^{-}$, $\mathcal{M}
\to\eta_{c}\eta^{(\prime)}$, and $\mathcal{ M} \to J/\psi\phi$. Partial widths
of these decays are determined by the strong couplings $g_i, \ i=1,2,3,4 $ at
vertices $\mathcal{M} D_{s}^{+}D_{s}^{-}$, $\mathcal{M}\eta_{c}
\eta^{(\prime)}$, and $\mathcal{M} J/\psi\phi$. They are computed by means of
the three-point sum rule method. Predictions for the mass $m=(4117 \pm
85)~\mathrm{MeV}$ and width $\Gamma_{ \mathcal{M}}=(62 \pm 12)~\mathrm{MeV}$ of
the molecule $\mathcal{M}$ are compared with the corresponding LHCb data, and
also with our results for the diquark-antidiquark state
$X=[cs][\overline{c}\overline{s}]$. We argue that the structure $X_0(4140)$ may
be interpreted as the hadronic molecule $ D_s^{+}D_s^{-}$, whereas the
resonance $X(3960)$ can be identified with the tetraquark $X$.
