  The top quark flavor changing neutral current processes are extremely
suppressed within the Standard Model. Nevertheless, they could be enhanced in a
new physics model beyond the Standard Model. Investigating the top quark's
flavor changing neutral current interactions at colliders would be an important
test in terms of new physics. In this work, we examine the potentials of the
processes ${e^{-}} {p} {\rightarrow} {e^{-}} {\gamma}^{*} {p} {\rightarrow}
{e^{-}} W^{+} b {\gamma}^{*}{\rightarrow} {e^{-}} {j} {\bar{j}} b {\gamma}^{*}
$ and ${e^{-}} {p} {\rightarrow} {e^{-}} {\gamma}^{*} {p} {\rightarrow} {e^{-}}
W^{+} b {\gamma}^{*}{\rightarrow} {e^{-}} \textit{l} {\nu}_\textit{l} b
{\gamma}^{*} $ at the FCC-eh with $\sqrt{s} = 7.08 $ and $ 10.0 TeV $ to study
anomalous $tq\gamma$ couplings via effective Lagrangians. We obtain $95{\%}$
confidence level sensitivities on the anomalous coupling parameters at the
three FCC-eh energies and various integrated luminosities. We find that our
limits are at least two orders of magnitude better than the current LHC
experimental results.
