The Luttinger Hamiltonian model is employed to investigate spin–orbit magneto-transport in an indium arsenide-based p-type double top-gate device with Rashba and Zeeman effects. The analyses focus particularly on the effects of the top-gate width (L), distance between the top gates (d), potential energy amplitude (U0), and asymmetry of the top-gate width on the formation of electron-like quasi-bound states and hole-like quasi-bound states within the conduction channel. The results confirm the feasibility of controlling the transport characteristics of the charged carriers through an appropriate setting of the gate width and gate potential energy. The findings provide useful insights into the complex transport dynamics of p-type semiconductor systems and have potential implications for device engineering. •The Luttinger Hamiltonian model is employed to investigate spin–orbit magneto-transport in an InAs-based p-type double top-gate device.•The analyses focus particularly on the effects of the top-gate width (L), distance between the top gates (d), potential energy amplitude (U0), and asymmetry of the top-gate width on the formation of electron-like quasi-bound states and hole-like QBSs.•The results confirm the feasibility of controlling the transport characteristics of the charged carriers through an appropriate setting of the gate width and gate potential energy.