Photon-like particles are predicted in many extensions of the Standard Model. They have interactions similar to the photon, are vector bosons, and can be produced together with photons. The present paper proposes a search for such particles in the $e^{+}{e}^{-}\to U\gamma$ process in a positron-on-target experiment, exploiting the positron beam of the DA$\Phi$NE linac at the Laboratori Nazionali di Frascati, INFN. In one year of running a sensitivity in the relative interaction strength down to ~10−6 is achievable, in the mass region from 2.5 $\text{MeV}<M_U<20$ MeV. The proposed experimental setup and the analysis technique are discussed.