A totally asymmetric exclusion process consisting of classical particles with next-nearest-neighbor interactions has been considered on a 1D discrete lattice with a ring geometry. Using large deviation techniques, we have investigated fluctuations of particle current in two and three-particle sectors. In a two-particle sector, we have obtained exact large deviation function for the probability distribution of particle current. In this sector, we have also calculated the the propensity of each configuration to exhibit atypical particle current. Analytical results for both the scaled cumulant generating function of particle current and average particle current are compared with those obtained from cloning Monte Carlo simulations. Numerical results in three-particle sector have also been presented.
