We investigate the $B^0\to J/\psi \eta K^0$ and $B^{+}\to J/\psi \eta K^{+}$ decay by using the Dalitz plot analysis. As we know there are tree, penguin, emission, and emission-annihilation diagrams for these decay modes in the factorization approach. The transition matrix element is factorized into a $B\to \eta K$ form factor multiplied by $J/\psi$ decay constant and also a $B\to K$ form factor multiplied by $J/\psi \eta$ decay constant. According to QCD factorization approach and using the Dalitz plot analysis, we calculate the branching ratios of the $B^0\to J/\psi \eta K^0$ and $B^{+}\to J/\psi \eta K^{+}$ three-body decay in view of the $\eta -\eta \text{'}$ mixing and obtain the value of the $\left(9.22_{-1.47}^{+2.67}\right)\times 10^{-5}$, while the experimental results of them are $(8\pm 4)\times 10^{-5}$ and $(10.8\pm 3.3)\times 10^{-5}$, respectively. In this research we also analyze the $B\left(B_s\right)\to {\eta }_c\pi K^{*}$ decay which is similar to the previous decay, but there is no experimental data for the last decay. Since for calculations of the $B\left(B_s\right)\to {\eta }_c\pi K^{*}$ decay we use assumptions of the $B\to J/\psi \eta K$ decay, we hope that if this decay will be measured by the LHCb in the future, the experimental results will be in agreement with our calculations.