  In this article, 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 take
into account our previous calculations and 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 $X(3912)$ and $X(4500)$ as the 1S and 2S
$[cs]_A[\bar{c}\bar{s}]_A$ tetraquark states respectively with the
$J^{PC}=0^{++}$.
