This paper is primarily focused on developing an analytical model to mimic the synaptic behavior with non-zero bandgap of boron (B)/nitrogen (N) substitution doped graphene field effect transistors (GFET). The trap charges at the channel and gate-insulator interface are utilized to induce the hysteresis conduction mechanism, which further is exploited to accomplish the synaptic plasticity. The proposed recurrence i.e., time dependent trap states drain current model is well capturing the physical insights of trap charges through an equivalent MIG (metal-insulator-graphene) model. The interesting fact of the proposed model is that it is compatible with both the doped (B/N) as well as with the undoped GFET. The model is also explored to generate the hysteresis characteristics of the GFET that is further utilized for mimicking the synaptic behavior. Another fact needs to be noticed is the existence of complete off regions for doped B/N GFET unlike the undoped case that manifests the undesirable ambipolar behaviour. As a result, the synapse made up of B/N doped GFET is predicting an optimistic learning and memory mechanism, termed as spike time dependent plasticity (STDP). The STDP characteristics of B/N doped synaptic GFET has been enhanced by more than 18$\times$ when compared against the artificial synapse made by undoped GFET. Hence, the hysteresis behaviour along with non-zero bandgap of B/N substitution doped GFETs make it highly favourable in dynamic mimicking of synaptic plasticity with efficient biologically plausible.