Associated quarkonia production in a single boson $e^{+}{e}^{-}$ annihilation

The production cross sections of charmonia, charmonium-bottomonium and bottomonia pairs in a single boson $e^{+}{e}^{-}$ annihilation have been studied in a wide range of energies, which will be achieved at future $e^{+}{e}^{-}$ colliders such as ILC and FCC. One loop QCD corrections to QCD and EW contributions as well as their interference are considered. The both intermediate bosons $\gamma$ and $Z$ are taken into account.