The next generation of water Cherenkov neutrino telescopes in the Mediterranean Sea are under construction offshore France (KM3NeT/ORCA) and Sicily (KM3NeT/ARCA). The KM3NeT/ORCA detector features an energy detection threshold which allows to collect atmospheric neutrinos to study flavour oscillation. This paper reports the KM3NeT/ORCA sensitivity to this phenomenon. The event reconstruction, selection and classification are described. The sensitivity to determine the neutrino mass ordering was evaluated and found to be 4.4 $$\sigma $$ $\sigma$ if the true ordering is normal and 2.3 $$\sigma $$ $\sigma$ if inverted, after 3 years of data taking. The precision to measure $$\varDelta m^2_{32}$$ $\Delta m_{32}^2$ and $$\theta _{23}$$ ${\theta }_{23}$ were also estimated and found to be $$85 . 10^{-6}~{\mathrm{eV}^{2}}$$ $85.{10}^{-6}{\mathrm{eV}}^2$ and $$(^{+1.9}_{-3.1})^{\circ }$$ ${{(}_{-3.1}^{+1.9})}^{\circ }$ for normal neutrino mass ordering and, $$75 . 10^{-6}~{\mathrm{eV}^{2}}$$ $75.{10}^{-6}{\mathrm{eV}}^2$ and $$(^{+2.0}_{-7.0})^{\circ }$$ ${{(}_{-7.0}^{+2.0})}^{\circ }$ for inverted ordering. Finally, a unitarity test of the leptonic mixing matrix by measuring the rate of tau neutrinos is described. Three years of data taking were found to be sufficient to exclude event rate variations larger than 20% at $$3\sigma $$ $3\sigma$ level.