  We apply the method of QCD sum rules to study the structure $X$ newly
observed by the BESIII Collaboration in the $\phi \eta^\prime$ mass spectrum in
2.0-2.1 GeV region in the $J/\psi \rightarrow \phi \eta \eta^\prime$ decay. We
construct all the $s s \bar s \bar s$ tetraquark currents with $J^{PC} =
1^{+-}$, and use them to perform QCD sum rule analyses. One current leads to
reliable QCD sum rule results and the mass is extracted to be
$2.00^{+0.10}_{-0.09}$ GeV, suggesting that the structure $X$ can be
interpreted as an $s s \bar s \bar s$ tetraquark state with $J^{PC} = 1^{+-}$.
The $Y(2175)$ can be interpreted as its $s s \bar s \bar s$ partner having
$J^{PC} = 1^{--}$, and we propose to search for the other two partners, the $s
s \bar s \bar s$ tetraquark states with $J^{PC} = 1^{++}$ and $1^{-+}$, in the
$\eta^\prime f_0(980)$, $\eta^\prime K \bar K$, and $\eta^\prime K \bar K^*$
mass spectra.
