As power systems move towards decentralized models based on renewable energy sources with distributed generation, the role of power inverters in microgrids becomes increasingly important. In this paper, a three-level T-type quasi-impedance source inverter (3L-T-type qZSI) with a grid-forming control structure is studied for the first time in an islanded ac microgrid composed by three prosumers, supplying residential loads. The power sharing among prosumers is achieved through the well-known droop control method with virtual impedance, and proportional-resonant (PR) controller-based voltage and current control loops. A proportional-integral (PI) based control for regulating the dc-link voltage of the T-Type inverter was implemented making use of the boost ability of the qZS network. The proper operation of the microgrid has been tested by simulation with PLECS, demonstrating a robust behavior of the overall system and a good dynamic performance of the proposed control structure for the 3L-T-Type qZSI in different conditions.