  We study composite electron production at the FCC-based three electron-proton
colliders with the center-of-mass energies of $3.46$, $10$ and $31.6$ TeV. For
the signal process of $ep\rightarrow e^{\star}X\rightarrow e\gamma X$ , the
production cross-sections and decay widhts of the excited electrons have been
calculated. The differences of some kinematical quantities of the final state
particles between the signal and background have been analyzed. For this
purpose, transverse momentum and pseudorapidity distributions of electron and
photon have been obtained and the kinematical cuts for discovery of the excited
electrons have been assigned. We have finally determined the mass limits of
excited electrons for observation and discovery by applying these cuts. It is
shown that the mass limit for discovery obtained from the collider with
$\sqrt{s}=31.6$ TeV (called PWFA-LC$\otimes$FCC) is $22.3$ TeV for the
integrated luminosity $L_{int}=10$ $fb^{-1}$.
