The critical role of energy consumption in biological systems including T cell discrimination process has been investigated in various ways. The kinetic proofreading (KPR) in T cell recognition involving different levels of energy dissipation influences functional outcomes such as error rates and specificity. In this work, we study quantitatively how the energy cost influences error fractions, sensitivity, specificity, kinetic speed in terms of Mean First Passage Time (MFPT) and adaption errors. These provide the background to adequately understand T cell dynamics. It is found that energy plays a central role in the system that aims to achieve minimum error fractions and maximum sensitivity and specificity with the fastest speed under our kinetic scheme for which numerical values of kinetic parameters are specially chosen, but such a condition can be broken with varying data. Starting with the application of steady state approximation (SSA) to the evaluation of the concentration of each complex produced associated with KPR, which is used to quantify various observables, we present both analytical and numerical results in detail.