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We study composite electron production at the FCC-based three electron-protoncolliders with the center-of-mass energies of $3.46$, $10$ and $31.6$ TeV. Forthe signal process of $ep\rightarrow e^{\star}X\rightarrow e\gamma X$ , theproduction cross-sections and decay widhts of the excited electrons have beencalculated. The differences of some kinematical quantities of the final stateparticles between the signal and background have been analyzed. For thispurpose, transverse momentum and pseudorapidity distributions of electron andphoton have been obtained and the kinematical cuts for discovery of the excitedelectrons have been assigned. We have finally determined the mass limits ofexcited electrons for observation and discovery by applying these cuts. It isshown 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 theintegrated luminosity $L_{int}=10$ $fb^{-1}$.

Single production of the excited electrons at the future FCC-based lepton-hadron colliders