As Chronos has said, not applicable, since in the case of photons it’s not applicable. Photons do carry momentum. Those “Crookes Radiometer/Light Mills” were a 19th century atempt to directly observe this momentum. It didn’t work, mainly because they couldn’t get a good enough vacuum (and the rotation they observed had a different, and surprisingly complex, cause), but direct observation of light momentum was made in the 1930s. With the advent of laser beams, the momentum of light was significantly boosted by the greater intensity (and, for some effects, coherence), and people were able to levitate small balls and thin films. I’ve seen the (unintended) effect in my own lab. Such momentum transfer is behind the principle of Light Sails,
The momentum of a photon is prooportional to its wavenumber (and its frequency), and this changes with reflection from a moving reflector, so you certainly can cause reflected photons to have different momentum from he incident photons, even at speeds well below relativistic speeds.