Solar photovoltaic (SPV)-based microgrid systems have established themselves as the novel clean and green solution to climate change. Thus, research is oriented toward a viable and universal solution to renewable energy based power generation. Though much progress is made in this frontier, there are still specific problems in the conventional control approach. Set-point controllers, an easy choice for control architecture, fail to satisfy the intermittent natured SPV source, compelling to look for a dynamic gain tuning technique to overcome stability margin issues. In this article, a graph signal processing least mean <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</i> th (GNLMP) adaptive current control method is introduced, which is computationally fast, robust, and improves the power quality (PQ) of the injected utility current. A microgrid, by definition, must possess the facility to work in an islanded mode to supply local commodities whenever there is a utility outage or utility faults and resynchronizes to the utility when the grid codes are in match according to the IEEE-519 std. Synchronization is demonstrated here using a more stable enhanced phase-locked loop (Ms-EPLL) technique, a modified version of EPLL. The PLL technique is more stable than EPLL by adding nonlinear term in each of phase and amplitude line. The GNLMP current control and Ms-EPLL synchronization technique are verified for acceptable steady-state and dynamic behavior via tests performed on an experimental setup. Seamless transfer synchronization and meeting PQ as the IEEE-519 std., i.e., total harmonic distortion <5%, are the significant outcome of this article.