  In this article, we take into account our previous calculations based on the
QCD sum rules, and tentatively assign the $X(4630)$ as the
$D_s^*\bar{D}_{s1}-D_{s1}\bar{D}_s^*$ tetraquark molecular state or
$[cs]_P[\bar{c}\bar{s}]_A+[cs]_A[\bar{c}\bar{s}]_P$ tetraquark state with the
$J^{PC}=1^{-+}$, and assign the $X(3915)$ and $X(4500)$ as the 1S and 2S
$[cs]_A[\bar{c}\bar{s}]_A$ tetraquark states respectively with the
$J^{PC}=0^{++}$. Then we extend our previous works to investigate the LHCb's
new tetraquark candidate $X(4685)$ as the first radial excited state of the
$X(4140)$ with the QCD sum rules, and obtain the mass
$M_{X}=4.70\pm0.12\,\rm{GeV}$, which is in very good agreement with the
experimental value $4684 \pm 7 {}^{+13}_{-16}\,\rm{MeV}$. Furthermore, we
investigate the two-meson scattering state contributions in details, and
observe that the two-meson scattering states alone cannot saturate the QCD sum
rules, the contributions of the tetraquark states play an un-substitutable
role, we can saturate the QCD sum rules with or without the two-meson
scattering states.
