We apply the method of QCD sum rules to study the structure X newly observed by the BESIII Collaboration in the φη mass spectrum in 2.0-2.1 GeV region in the J/ψ → φηη decay. We construct all the ssss 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 ssss tetraquark state with J PC = 1 +−. The Y (2175) can be interpreted as its ssss partner having J PC = 1 −− , and we propose to search for the other two partners, the ssss tetraquark states with J PC = 1 ++ and 1 −+ , in the η f 0 (980), η KK , and η KK * mass spectra.