  The kink structure in band dispersion usually refers to a certain
electron-boson interaction, which is crucial in understanding the pairing in
unconventional superconductors. Here we report the evidence of the observation
of a kink structure in Fe-based superconductor CsCa$_2$Fe$_4$As$_4$F$_2$ using
angle-resolved photoemission spectroscopy. The kink shows an orbital selective
and momentum dependent behavior, which is located at 15 meV below Fermi level
along the Gamma-M direction at the band with dxz orbital character and vanishes
when approaching the Gamma-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 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.
