  We investigate the possible presence of Flavor Changing Neutral Current
(FCNC) couplings of the top quark with gluon and photon through $e^-p\to e^-tj$
process at the Future Circular Collider in the proton-electron mode (FCC-he).
Focusing on disentangling the effects of different couplings that could be
present, we exploit the presence of the scattered electron, the angular
distribution of which is sensitive to the type of coupling involved. Top quark
polarisation accessed through the angular distribution of the decay lepton
provides additional handle in identifying the nature of the couplings. Further,
we demonstrate the potential of electron beam polarisation in distinguishing
the left-handed and right-handed couplings of both gluon and photon separately.
Considering an $e^-p$ collider of beam energies of $E_{e(p)} = 60~(50000)$~GeV
at 2~ab$^{-1}$ integrated luminosity, couplings can be probed at the level of
$10^{-2}$ with the corresponding branching fractions of ${\rm BR}(t\to
u\gamma)\le 4 - 7 \times 10^{-6}$ and ${\rm BR}(t\to c\gamma) \le 1-2 \times
10^{-5}$, depending on if the coupling is right-handed or left-handed. The
corresponding limits on the gluon couplings lead to ${\rm BR}(t\to ug)\le 1.7
\times 10^{-5}$ and ${\rm BR}(t\to cg) \le 3-4 \times 10^{-5}$.
