This study introduces a new three-dimensional space vector modulation technique for a fourleg quasi Z-source inverter (4L-qZSI) integrating a qZSN and a two-level four-leg inverter. The proposed method encompasses three variants, namely 3DZSVM2, 3DZSVM4, and 3DZSVM8, designed to enhance steady-state operations and harmonic distortions for 4L-qZSI. One of the main contributions of this research is the establishment of a new modulation technique for the 4L-qZSI. The proposed method amalgamates the benefits of SVMs in both abc and αβγ coordinates. The design processes of the 3DZSVM algorithm are carried out in the newly proposed ρστ coordinates, while the space vector diagram (SVD) of the 4L-qZSI is utilized in the αβγ location. The proposed algorithm is applied in a single sector, optimizing time interval calculations and pulse creation without requiring trigonometric functions. Extensive simulation studies were conducted to validate the performance of the introduced modulation scheme for the 4L-qZSI. The simulation results show excellent steady-state performance and benefit over the conventional space vector modulation with zero sequences (CZPWM), including a power loss reduction of 50% and a 50% decrease in the THD of the output voltage. In addition, applying this technique results in enhanced output current quality, reduced power loss by 40%, and decreased inductive current ripple by 50% under unbalanced load conditions. Furthermore, the proposed 3DZSVM control strategy for 4L-qZSI is experimentally verified using the TMS320F28379D kit based on the Hardware-in-the-Loop (HIL) simulator. This demonstrates the practicality and effective performance of the suggested control strategy under unbalanced load conditions.