  We study features of the resonances $X(2100)$ and $X(2239)$ by treating them
as the axial-vector and vector tetraquarks with the quark content $ss
\overline{s}\overline{s}$, respectively. The spectroscopic parameters of these
exotic mesons are calculated in the framework of the QCD two-point sum rule
method. Obtained prediction for the mass $m=(2067 \pm 84)~\mathrm{MeV}$ of the
axial-vector state is in excellent agreement with the mass of the structure
$X(2100)$ recently observed by the BESIII Collaboration in the decay $J/\psi
\to \phi \eta \eta^{\prime}$ as the resonance in the $\phi \eta^{\prime}$ mass
spectrum. We explore also the $S$-wave decays $X(2100) \to \phi\eta^{\prime}$
and $X(2100) \to \phi \eta$ using the QCD light-cone sum rule approach and
technical methods of the soft-meson approximation. The width of the
axial-vector tetraquark, $\Gamma=(130.2\pm 30.1)~\mathrm{MeV}$, saturated by
these two decays is comparable with the measured full width of the resonance
$X(2100)$. Our prediction for the vector $ss\overline{s}\overline{s }$
tetraquark's mass $\widetilde{m}=(2283\pm 114)~\mathrm{MeV}$ is consistent with
the experimental result $2239.2 \pm 7.1 \pm 11.3~\mathrm{MeV}$ of the BESIII
Collaboration for the mass of the resonance $X(2239)$.
