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We analyze the prospects for detection of light sub-GeV dark matter producedin experiments designed to study the properties of neutrinos, such asMiniBooNE, T2K, SHiP, DUNE etc. We present an improved production model, whendark matter couples to hadronic states via a dark photon or baryonic vectormediator, incorporating bremsstrahlung of the dark vector. In addition toelastic scattering, we also study signatures of light dark matter undergoingdeep inelastic or quasi-elastic NC$\pi^0$-like scattering in the detectorproducing neutral pions, which for certain experiments may provide the bestsensitivity.  An extensive appendix provides documentation for a publicly availablesimulation tool {\tt BdNMC} that can be applied to determine the hidden sectordark matter production and scattering rate at a range of proton fixed targetexperiments.

Light dark matter in neutrino beams: production modelling and scattering signatures at MiniBooNE, T2K and SHiP