We calculate the next-to-leading order (NLO) QCD corrections to $\ensuremath{\gamma}+\ensuremath{\gamma}\ensuremath{\rightarrow}{\ensuremath{\eta}}_{c}+c+\overline{c}$, $\ensuremath{\gamma}+\ensuremath{\gamma}\ensuremath{\rightarrow}{\ensuremath{\eta}}_{b}+b+\overline{b,}$ and $\ensuremath{\gamma}+\ensuremath{\gamma}\ensuremath{\rightarrow}{B}_{c}+b+\overline{c}$ processes in the framework of nonrelativistic QCD factorization formalism. The cross sections at the SuperKEKB electron-positron collider, as well as the future collider like the Circular Electron Positron Collider, are evaluated. Numerical results indicate that the NLO corrections are significant, and the uncertainties in theoretical predictions with NLO corrections are reduced as expected. Due to the high luminosity of the SuperKEKB collider, the ${\ensuremath{\eta}}_{c}+c+\overline{c}$ production is hopefully observable in the near future.