We construct a radiative neutrino mass model that combines the scotogenic mechanism with modular $S_4$ flavour symmetry. The entire lepton flavour structure is governed by holomorphic modular forms of a single complex modulus $\tau$, eliminating the need for flavon fields. Beyond the Standard Model, the particle content consists of two right-handed Majorana fermions assigned to the $S_4$ doublet representation and an inert scalar doublet odd under a ${\mathbb{Z}}_2$ parity. Neutrino masses emerge at one loop through the scotogenic mechanism, and the lightest ${\mathbb{Z}}_2$-odd state serves as a dark matter candidate. A comprehensive scan of the parameter space demonstrates consistency with all five neutrino oscillation observables at the $3\sigma$ level. Having exactly two right-handed neutrinos forces the light neutrino mass matrix to rank two, leaving one neutrino massless and selecting normal ordering as the only viable option. The framework predicts a total neutrino mass in the narrow window $\sum m_{\nu }\simeq 0.059$–$0.06eV$, well within current cosmological bounds, and an effective Majorana mass $m_{\beta \beta }\simeq (1.3$–$3.5)\times {10}^{-3}eV$ relevant for neutrinoless double beta decay searches. The structure of the right-handed Majorana mass matrix, together with the phenomenologically relevant regime $M_{ϵ}\ll M$, yields a quasi-degenerate heavy-neutrino spectrum, enabling flavoured resonant leptogenesis at $M_1\sim {10}^{5}GeV$. Integration of the full three-flavour Boltzmann equations confirms that the observed baryon asymmetry is reproduced, establishing that neutrino masses, leptonic mixing, and the baryon asymmetry of the Universe all find a common explanation within this framework.