In this work, room-temperature-processed amorphous InGaZnO (a-IGZO) thin-film transistors (TFTs) have been fabricated with high-k HfLaO as gate dielectric for synaptic devices. By raising the indium content in the a-IGZO film via co-sputtering and treating the HfLaO gate dielectric in an Ar plasma, the TFT with In1.0Ga3.0Zn0.4O2.1 presents excellent electrical characteristics: a high intrinsic carrier mobility of 45.8 cm2/V·s, a small threshold voltage of 1.93 V, a small hysteresis of -0.015 V, and a small subthreshold swing (SS) of 0.21 V/dec. Although the oxygen vacancies in the In1.0Ga3.0Zn0.4O2.1 TFT are increased to produce a high carrier mobility, memristive behaviors are hardly observed under zero gate bias due to their occupied states. Various conductance modulations and synaptic plasticities are achieved under a 2-V drain spiking voltage and a small gate bias of 1 V due to migration of oxygen ions and emptying/detrapping of oxygen vacancies in the In1.0Ga3.0Zn0.4O2.1 film, resulting in a concurrent emulation of neurotransmitter and neuromodulator through exploiting the native 3-terminal structure of the TFT.