Using angle-resolved photoemission spectroscopy, we report the evidence of the observation of a kink structure in the band dispersion of Fe-based superconductor CsCa2Fe4As4F2. The kink shows an orbital selective and momentum dependent behavior, which is located at 15 meV below Fermi level along the Γ - M direction at the band with dxz orbital character and vanishes when approaching the Γ - X direction, correlated with a slight decrease of the superconducting gap. Most importantly, this kink structure disappears when the superconducting gap closes, indicating that the corresponding bosonic mode (~ 9 ± 1 meV) is closely related to superconductivity. However, the origin of this mode remains unidentified, since it cannot be related to phonons or the spin resonance mode (~ 15 meV) observed by inelastic neutron scattering. The behavior of this mode is rather unique and challenges our present understanding of the superconducting paring mechanism of the bilayer FeAs-based superconductors.