Friedel Oscillations of Vortex Bound States under Extreme Quantum Limit in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi>KCa</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi>Fe</mml:mi></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:msub><mml:mrow><mml:mi>As</mml:mi></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:…

We report the observation of discrete vortex bound states with energy levels deviating from widely believed ratio 1:3:5 in vortices an iron based superconductor KCa2Fe4As4F2 through scanning tunneling microcopy (STM). Meanwhile Friedel oscillations are also observed for first time related vortices. By doing self-consistent calculations Bogoliubov-de Gennes equations, we find that at extreme quantum limit, superconducting order parameter exhibits a Friedel-like oscillation, which modifies and explains why it deviates 1:3:5. The can be roughly interpreted by theoretical calculations, however some features high energies could not explained. attribute this discrepancy to influence nearby impurities. Our combined STM measurement illustrate generalized feature type-II superconductors.