Abstract This paper explores the impact of orbital angular momentum (OAM) in composite vortex light on the absorption and dispersion characteristics of a weak probe light interacting with a single-layer graphene system. Through systematic investigation, we demonstrate the exceptional control achievable over absorption and dispersion profiles by manipulating the OAM of light. Under resonance conditions for the probe light, transparent regions emerge in the spatial profile of probe absorption, and the number of these transparent regions can be precisely regulated by adjusting the OAM number of the composite vortex light. Conversely, in the case of off-resonance probe light, amplified regions surface in the absorption spectrum, with the number of these regions controllable by the OAM state of the composite vortex light. These findings hold significant implications for optical communication systems, offering a valuable tool for the detection and measurement of the OAM number of composite vortex light, and paving the way for advancements in tailored signal processing and communication technologies.