In this work, we introduce an explicit P-wave to construct the diquarks \([qc]_{\widehat{V}}\) , then construct the local four-quark currents to explore the hidden-charm tetraquark states with the \(J^{PC}=0^{++}\) , \(1^{+-}\) , and \(2^{++}\) in the framework of the QCD sum rules at length. Our calculations indicate that the light-flavor SU(3) breaking effects on the tetraquark masses are tiny. The predictions support assigning the X(4475) and X(4500) as the \([uc]_{\widehat{V}}[\overline{uc}]_{\widehat{V}}-[dc]_{\widehat{V}}[\overline{dc}]_{\widehat{V}}\) and \([sc]_{\widehat{V}}[\overline{sc}]_{\widehat{V}}\) tetraquark states with the \(J^{PC}=0^{++}\) respectively, and assigning the \(Z_{c}(4600)\) and \(Z_{\bar{c}\bar{s}}(4600)\) as the \([uc]_{\widehat{V}}[\overline{dc}]_{\widehat{V}}\) and \([qc]_{\widehat{V}}[\overline{sc}]_{\widehat{V}}\) tetraquark states with the \(J^{PC}=1^{+-}\) respectively. On the other hand, there is no room for the X(4710) and X(4700). Combined with previous works, the X(4475), X(4500), \(Z_{c}(4600)\) , and \(Z_{\bar{c}\bar{s}}(4600)\) might have other important Fock components besides the \(\widehat{V}\widehat{V}\) type components.
