In a multilevel quasi-impedance source inverter (qZSI), phase-shifted carrier pulsewidth modulation (PS-PWM) is the most popular modulation method as it offers advantages such as simple implementation and evenly powered distribution among all qZSI modules with optimum total harmonic distortion (THD). However, it results in higher switching losses. An approach to solving this problem would be development and implementation of a PWM method which results in lower switching losses. With this aim, a novel hybrid phase-opposition disposed, phase-shifted (PWM) (PODPS-PWM) technique is proposed in this article. With the proposed PWM method, reduced switching losses are achieved. Active state losses are reduced to 6% and switching losses are reduced to at least >39% in qZSI modules. A mathematical relationship between the PS-PWM and the proposed PODPS-PWM has been deduced. For experimental validation, a 1.5-kW seven-level qZSI setup is developed. Different performance aspects are presented, discussed, and analyzed, which help in validating the superior performance of the proposed solution. Moreover, an application for the solar photovoltaic (PV) multilevel inverter system has been discussed, for the partial shading condition. During this condition, the PS-PWM forces the extraction of lower power from the remaining healthy modules. This is due to the evenly powered distribution nature of the PS-PWM. Comparatively, the proposed PWM yields higher power. To validate higher power extraction, simulation results are presented and compared for both modulations under healthy and different partially shaded conditions. Under extreme partial shading conditions, the increase in power extraction is up to 29%.