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Inspired by the similarity of mass gaps of $J/\psi$ and $\Upsilon$ families,the prediction of missing higher charmonium with mass $4263$ MeV and verynarrow width is made. In addition, the properties of two charmonium-likestates, $X(3940)$ and $X(4160)$, and charmonium $\psi(4415)$ are discussed.Here, $X(3940)$ as $\eta_c(3S)$ is established while the explanation of$X(4160)$ to be $\eta_c(4S)$ is fully excluded and $\eta_c(4S)$ is typically avery narrow state. These predictions can be accessible at BESIII, Belle andBelleII in near future.

Prediction of a missing higher charmonium around 4.26 GeV in $J/\psi$ family