Single vector-like B quark (VLQ-B), predicted in numerous new physics scenarios beyond the Standard Model (SM), can be explored through their production in association with a top quark and an electron neutrino in high-energy \(e\gamma\) collisions, specifically via the process \(e \gamma \rightarrow \nu _e B \bar{t}\) . We investigate the discovery potential of this channel at a center-of-mass energy of 3 TeV, focusing on final states containing two b-jets and four light jets. By performing detailed simulations of the signal and relevant SM backgrounds, we present the \(3\sigma\) and \(5\sigma\) sensitivity reach in terms of parton-level parameter space regions for representative integrated luminosity scenarios. Our results demonstrate that VLQ-B can be discovered via this process within well-defined regions of the \(g^*-m_B\) parameter plane.
