Quantum transport properties of a large bandgap In0.15Al0.79Ga0.06N/GaN quaternary GaN high electron mobility transistor (HEMT) heterostructure are studied at low temperatures up to 2 K. Herein, we report the first evidence of weak localization in a quaternary GaN two-dimensional electron gas (2DEG) system. We observe negative magnetoresistance behavior and extracted dephasing time (τΦ) using a Hikami–Larkin–Nagaoka model at 2.2 K. Linear dependency of dephasing rate with temperature (τΦ−1∝T) is established below 20 K. Furthermore, Shubnikov–de Haas quantum oscillation induced by 2DEG is observed using perpendicular magnetic (B⊥) field strengths up to 14 T. From the temperature-dependent oscillation amplitude, we extracted an effective mass m*≈0.237me. The dominance of small-angle scattering in the 2DEG channel is identified from less than unit ratio (τq/τt≪1) of quantum lifetime (τq) to the Hall transport lifetime (τt). In our study, we have demonstrated that the In0.15Al0.79Ga0.06N/GaN quaternary heterostructure possesses high dephasing time (τΦ=5.4 ps) and larger quantum lifetime (τq=0.102 ps) indicating better suitability and a way forward to high-power–high-frequency GaN HEMT development.