  The current most stringent constraints for the existence of sub-GeV dark
matter coupling to Standard Model via a massive vector boson $A^\prime$ were
set by the NA64 experiment for the mass region $m_{A^\prime}\lesssim 250$ MeV,
by analyzing data from the interaction of $2.84\cdot10^{11}$ 100-GeV electrons
with an active thick target and searching for missing-energy events. In this
work, by including $A^\prime$ production via secondary positron annihilation
with atomic electrons, we extend these limits in the $200$-$300$ MeV region by
almost an order of magnitude, touching for the first time the dark matter relic
density constrained parameter combinations. Our new results demonstrate the
power of the resonant annihilation process in missing energy dark-matter
searches, paving the road to future dedicated $e^+$ beam efforts.
