We consider a simplified model containing a new neutral singlet scalar and a vector-like top quark, which mix with the Higgs boson and top quark of the SM, respectively. The presence of a vector-like top quark in addition to a new scalar, which is common in many new physics models, is well motivated as they help stabilize the electroweak vacuum of the Higgs potential in the SM. Beside the theoretical motivations, this model can explain the observed enhancements in the di-Higgs production at the LHC experiments. We propose that the associated production of the new singlet scalar with a photon at future electron-positron colliders could be one of the practical channels to search for new physics. We compute the production rate of the scalar plus a photon at the proposed high luminosity electron-positron colliders such as ILC and CLIC.