Searches for physics Beyond the Standard Model (BSM) can be carried out with precise and GeV-energy-range experiments. In many string theories, a Hidden Sector, decoupled to the SM, foresees the existence of a new massive boson, the A′ or heavy photon, that weakly couples to the electromagnetic current. A new particle with mass in the range of 1 MeV - 1 GeV could explain many astro-particle observations (e.g. positron excess seen by PAMELA and AMS experiments) and some anomalies not yet fully understood (e.g. muon g - 2 factor). The search for A′ has motivated intense experimental activities in almost every accelerator facility using different techniques: colliding beam, fixed target experiments, meson rare decays. Jefferson Lab, a world-leading nuclear physics laboratory, is planning a set of fixed target experiments aiming to discover the A′ or set new limits in its mass and coupling, with an unprecedented sensitivity and reach capability. In this contribution, after reviewing the physics case and some experimental evidences, I will report on the program of measurements planned at Jefferson Lab for the next years.