The top quark flavor changing neutral current (FCNC) processes are extremely suppressed within the standard model (SM), however they could be enhanced in a new physics model beyond the SM. The top quark FCNC interactions would be a good test of new physics at present and future colliders. For a wide framework of these models, these interactions can be described by the effective Lagrangian. In this work, we study tqγ and tqZ effective FCNC interaction vertices through the process e-p—>e-Wq+X at future hadron electron colliders LHeC and FCC-eh. The cross sections for the signal have been calculated for different values of parameters λu, λc for tqγ vertices and 𝜅u, 𝜅c for tqZ vertices. Studying relevant SM background we estimate the attainable range of parameters depending on the integrated luminosity and present contour plots of couplings according to different significance levels including detector simulation.