Around the nuclear Fermi momentum, there is a transition of nucleon momentum distribution n(k) in nuclear matter, i.e., from a constant to the $1/k^4$ nucleon momentum distribution. While nowadays the transition momentum of minority in asymmetric matter is rarely studied and thus undetermined. In the framework of the IBUU transport model, proton transition momentum in nuclei is first studied. It is found that the transition momentum of proton is sensitive to the ${\pi }^{-}/{\pi }^{+}$ ratio as well as the energetic photon production in neutron-rich nuclear reaction. This result may push the study of how the proton momentum is distributed in neutron-rich matter forward and help us to better understand the dynamics of both neutron-rich nuclear reactions and neutron stars.