We investigate the momentum distributions of \({\textrm{H}}_{4}^{3+}\) molecular ions by numerically solving the two-dimensional (2D) time-dependent Schrödinger equation (TDSE). For \({\textrm{H}}_{4}^{3+}\) , the ground state \(A'\) , current-carrying states \({\textrm{E}}^{+}\) and \({\textrm{E}}^{-}\) are considered. The results show that the photoelectron momentum distributions (PMDs) of different initial states are all caused by multi-center interference in the single-photon ionization process. The number of lobes of PMDs is also explained by the ultra-fast ionization model. However, in the right-rotating ( \(+\) ) circularly polarized (CP) laser field, the intensity of PMDs with \({\textrm{E}}^{+}\) state is significantly higher than that with \({\textrm{E}}^{-}\) state, which can be attributed to the fact that the laser pulses with different rotations can produce selective state-state transitions. In addition, the difference in the intensity of PMDs in the current-carrying states \({\textrm{E}}^{+}\) and \({\textrm{E}}^{-}\) can be well explained by the time evolution of the electron wave packet. These findings provide new insight for future studies in the dynamics of current-carrying states in ring molecules.
