<p>We investigate the optical response of a closed-loop three-level quantum dot molecule driven by a structured Laguerre-Gaussian field carrying orbital angular momentum (OAM). Owing to the intrinsic phase sensitivity of the closed-loop configuration, the spatial phase structure of the coupling beam directly imprints on the probe-field dynamics, leading to a strongly spatially dependent optical response. As a result, phenomena such as Autler-Townes splitting, probe absorption, and amplification without inversion arise under both resonant and off-resonant conditions, with their spectral characteristics governed by the sign and magnitude of the OAM index. This OAM-controlled modulation of the optical response reveals a mechanism for phase-engineered light-matter interaction in quantum dot molecules. The results highlight the potential of this solid-state platform for structured light based quantum photonics, including quantum information processing, tunable slow and fast light, and high capacity optical data storage.</p>