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We measure the branching fractions of ${B}^{0}\ensuremath{\rightarrow}J/\ensuremath{\psi}{\ensuremath{\eta}}^{(\ensuremath{'})}$ decays with the complete Belle data sample of $772\ifmmode\times\else\texttimes\fi{}{10}^{6}$ $B\overline{B}$ events collected at the $\ensuremath{\Upsilon}(4S)$ resonance with the Belle detector at the KEKB asymmetric-energy ${e}^{+}{e}^{\ensuremath{-}}$ collider. The results for the branching fractions are: $\mathcal{B}({B}^{0}\ensuremath{\rightarrow}J/\ensuremath{\psi}\ensuremath{\eta})=(12.3{\ifmmode\pm\else\textpm\fi{}}_{1.7}^{1.8}\ifmmode\pm\else\textpm\fi{}0.7)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$ and $\mathcal{B}({B}^{0}\ensuremath{\rightarrow}J/\ensuremath{\psi}{\ensuremath{\eta}}^{\ensuremath{'}})<7.4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$ at 90% confidence level. The $\ensuremath{\eta}\mathrm{\text{\ensuremath{-}}}{\ensuremath{\eta}}^{\ensuremath{'}}$ mixing …