The long baseline experiments provide a unique opportunity to probe new physics beyond the Standard Model. My talk will cover two topics. First, we consider the case of three active and one sterile neutrino, i.e., the (3 + 1) scenario, and study its imprint at long baseline experiment such as DUNE. We investigate the potential of DUNE to constrain the sterile parameter space through combined near-far detector fits with optimized beam tunes and both charged-neutral current channels. In addition, we present the sensitivities of experiments such as T2HK, DUNE, and P2O in distinguishing between the standard and sterile scenarios. We also examine the impact of energy resolution on both the standard unknowns and sterile neutrino parameters in the context of DUNE. Second, we consider an effective non-Hermitian Hamiltonian for three flavor neutrino oscillations with decay and show that the two Majorana phases couple with the off diagonal decay terms, appearing in oscillation probabilities. We then analyze their impact across different channels and on CP violation observables.