  Using the QCD sum rules we test if the new narrow structure, the X(4350)
recently observed by the Belle Collaboration, can be described as a
$J^{PC}=1^{-+}$ exotic $D_s^*D_{s0}^*$ molecular state. We consider the
contributions of condensates up to dimension eight, we work at leading order in
$\alpha_s$ and we keep terms which are linear in the strange quark mass $m_s$.
The mass obtained for such state is $m_{D_s^*{D}_{s0}^*}=(5.05\pm 0.19)$ GeV.
We also consider a molecular $1^{-+}, D^{*}{D}_0^{*}$ current and we obtain
$m_{D^*{D}_0^*}=(4.92\pm 0.08)$ GeV. We conclude that it is not possible to
describe the X(4350) structure as a $1^{-+} D_s^*{D}_{s0}^*$ molecular state.
