The diversity of brain functions depend on the release of neurotransmitters in chemical synapses. The back gated three terminal field effect transistors (FETs) are auspicious candidates for the emulation of biological functions to recognize the proficient neuromorphic computing systems. In order to encourage the hysteresis loops, we treated the bottom side of MoTe2 flake with deep ultraviolet light in ambient conditions. Here, we modulate the short-term and long-term memory effects due to the trapping and de-trapping of electron events in few layers of a MoTe2 transistor. However, MoTe2 FETs are investigated to reveal the time constants of electron trapping/de-trapping while applying the gate-voltage pulses. Our devices exploit the hysteresis effect in the transfer curves of MoTe2 FETs to explore the excitatory/inhibitory post-synaptic currents (EPSC/IPSC), long-term potentiation (LTP), long-term depression (LTD), spike timing/amplitude-dependent plasticity (STDP/SADP), and paired pulse facilitation (PPF). Further, the time constants for potentiation and depression is found to be 0.6 and 0.9 s, respectively which seems plausible for biological synapses. In addition, the change of synaptic weight in MoTe2 conductance is found to be 41% at negative gate pulse and 38% for positive gate pulse, respectively. Our findings can provide an essential role in the advancement of smart neuromorphic electronics.