This paper presents a novel integral terminal sliding mode control (ITSMC) algorithm compounded with Barrier Lyapunov's Function (BLF) for high precision output tracking objective of uncertain N-dimensional strict feedback class of non-linear systems subjected to non-infringement of system output constraint. Besides, the proposed algorithm also employs uncertainty and disturbance estimator (UDE) technique for abating the existence of unknown mismatched and matched uncertainties. Most of the preliminary SMC schemes encompass the UDE technique to cope with unknown matched uncertainties only. However, the presented method embodies the dynamic surface control (DSC) architecture to get rid of the matching architectural constraint in UDE approach as well as 'complexity explosion' concern in backstepping approach. Additionally, the introduced method also applies the notion of symmetric BLF to enforce strict bounds on output tracking deviation from its reference value. To emphasize on the strengths of devised methodology, two examples are simulated by comparing the derived outcomes with already existing techniques in literature.