We present a search at Jefferson Laboratory for new forces mediated by sub-GeV vector bosons with weak coupling $\alpha'$ to electrons. Such a particle $A'$ can be produced in electron-nucleus fixed-target scattering and then decay to an $e^+e^-$ pair, producing a narrow resonance in the QED trident spectrum. Using APEX test run data, we searched in the mass range 175--250 MeV, found no evidence for an $A'\to e^+e^-$ reaction, and set an upper limit of $\alpha'/\alpha \simeq 10^{-6}$. Our findings demonstrate that fixed-target searches can explore a new, wide, and important range of masses and couplings for sub-GeV forces.
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