We discuss two complementary strategies to search for light dark matter (LDM) exploiting the positron beam possibly available in the future at Jefferson Laboratory. LDM is a new compelling hypothesis that identifies dark matter with new sub-GeV hidden sector states, neutral under standard model interactions and interacting with our world through a new force. Accelerator-based searches at the intensity frontier are uniquely suited to explore it. Thanks to the high intensity and the high energy of the CEBAF (Continuous Electron Beam Accelerator Facility) beam, and relying on a novel LDM production mechanism via positron annihilation on target atomic electrons, the proposed strategies will allow us to explore new regions in the LDM parameters space, thoroughly probing the LDM hypothesis as well as more general hidden sector scenarios.