We investigate the possible production of a MeV-scale sterile fermion through the up-scattering of neutrinos on nuclei and atomic electrons at different facilities. We consider a phenomenological model that adds a new fermion to the particle content of the Standard Model and we allow for all possible Lorentz-invariant non-derivative interactions (scalar, pseudoscalar, vector, axial-vector and tensor) of neutrinos with electrons and first-generation quarks. We first explore the sensitivity of the DUNE experiment to this scenario, by simulating elastic neutrino-electron scattering events in the near detector. We consider both options of a standard and a tau-optimized neutrino beams, and investigate the impact of a mobile detector that can be moved off-axis with respect to the beam. Next, we infer constraints on the typical coupling, new fermion and mediator masses from elastic neutrino-electron scattering events induced by solar neutrinos in two current dark matter direct detection experiments, XENONnT and LZ. Under the assumption that the new mediators couple also to first-generation quarks, we further set constraints on the up-scattering production of the sterile fermion using coherent elastic neutrino-nucleus scattering data from the COHERENT experiment. Moreover, we set additional constraints assuming that the sterile fermion may decay within the detector. We finally compare our results and discuss how these facilities are sensitive to different regions of the relevant parameter space due to kinematics arguments and can hence provide complementary information on the up-scattering production of a sterile fermion.