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Several Beyond the Standard Model theories are proposed that fermions mighthave composite substructure. The existence of excited quarks is going to be thenoticeable proof for the compositeness of Standard Model fermions. For thisreason, excited quarks have been investigated by phenomenological andexperimental high energy physicists at various collider options for the lastfew decades. The Future Circular Collider (FCC) has been recently planned asparticle accelerator to be established at CERN. Beside the $\sqrt{s}$ = 100 TeVproton-proton collisions, the FCC includes electron-positron andelectron-proton collision options. Construction of linear $e^- e^+$ colliders(or dedicated e-linac) tangential to the FCC will afford an opportunity tohandle multi-TeV $ep$ and $\gamma p$ collisions. In this respect, we executed asimulation of the resonance production of the excited $u$ quark at the FCCbased $\gamma p$ colliders with choosing both the polarized and unpolarizedphoton beams. The findings revealed that the chirality structure of the$q^*$-$q$-$\gamma$ vertex can be determined by the photon beam polarization.The attainable mass limits of the excited $u$ quark reached the highest valueswhen the polarized photon beam was chosen. In addition, the ultimatecompositeness scale values can be handled by appropriate choice of the photonbeam polarization.

Resonance Production of Excited u-quark at the FCC Based $\gamma$ $p$ Colliders