  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
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 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.
