  We use data from the COHERENT CsI[Na] scintillation detector to constrain
sub-GeV leptophobic dark matter models. This detector was built to observe
low-energy nuclear recoils from coherent elastic neutrino-nucleus scattering.
These capabilities enable searches for dark matter particles produced at the
Spallation Neutron Source mediated by a vector portal particle with masses
between 2 and 400 MeV/c$^2$. No evidence for dark matter is observed and a
limit on the mediator coupling to quarks is placed. This constraint improves
upon previous results by two orders of magnitude. This newly explored parameter
space probes the region where the dark matter relic abundance is explained by
leptophobic dark matter when the mediator mass is roughly twice the dark matter
mass. COHERENT sets the best constraint on leptophobic dark matter at these
masses.
