We study sterile neutrino dark matter (DM) in a classically conformal U(1)’ extension of the Standard Model with three right-handed neutrinos and a Majoron-like singlet scalar that generate the observed pattern of active neutrino masses and mixing via the type-I seesaw mechanism. Working in the regime of strongly suppressed active-sterile mixing, we show that the observed DM abundance can be produced through freeze-in from feeble interactions mediated by the heavy Z’ and the conformal scalar. We solve the Boltzmann equation for the nonthermal phase-space distribution and confront the scenario with Lyman-$\alpha$ and strong gravitational lensing data by computing the matter power spectrum. For keV-mass sterile neutrinos we identify the viable parameter space consistent with the inferred relic density and structure-formation and X-ray bounds, including regions compatible with a tentative 3.5 keV line. If a second sterile state is long-lived, late decays can realize a two-component setup that alleviates the S_8 tension. However, explanations of the 3.5 keV line and the S_8 tension are incompatible with the strong-lensing limit from JWST if the neutrinos saturate the relic abundance. In a highly fine-tuned variant of the model, the 220 PeV KM3NeT event can also be explained by invoking the decay of a superheavy sterile neutrino.