This study investigates the transport properties of two finite armchair graphene nanoribbons (A-GNRs) connected to semi-infinite leads, using a single π-band tight binding Hamiltonian and Green's function formalism. The research explores how geometric confinement and an external magnetic field influence the density of states (DOS) and conductance of these systems. The results show resonant tunneling behavior and periodic modulations in transport properties, with Aharonov-Bohm-type interference observed as periodic metal-semiconductor transitions in the DOS and conductance curves. The study considers different configurations of the nanoribbons, including symmetric and asymmetric widths and lengths, and examines the effects of varying the magnetic flux. The findings indicate that the magnetic field induces periodic metal-semiconductor transitions, which could have implications for electronic applications. The research also highlights the importance of quantum interference effects in these annular conductors, demonstrating the potential for tuning transport properties through geometric and magnetic parameters. The study is valid under low temperature conditions and in the absence of strong disorder.This study investigates the transport properties of two finite armchair graphene nanoribbons (A-GNRs) connected to semi-infinite leads, using a single π-band tight binding Hamiltonian and Green's function formalism. The research explores how geometric confinement and an external magnetic field influence the density of states (DOS) and conductance of these systems. The results show resonant tunneling behavior and periodic modulations in transport properties, with Aharonov-Bohm-type interference observed as periodic metal-semiconductor transitions in the DOS and conductance curves. The study considers different configurations of the nanoribbons, including symmetric and asymmetric widths and lengths, and examines the effects of varying the magnetic flux. The findings indicate that the magnetic field induces periodic metal-semiconductor transitions, which could have implications for electronic applications. The research also highlights the importance of quantum interference effects in these annular conductors, demonstrating the potential for tuning transport properties through geometric and magnetic parameters. The study is valid under low temperature conditions and in the absence of strong disorder.