<p>This study presents a theoretical investigation of second harmonic generation (SHG) resulting from the nonlinear interaction of a q-Gaussian laser beam with an anharmonic clustered plasma. The incident laser interacts with anharmonic atomic clusters, leading to the ionization of cluster atoms, and the formation of dense plasma spheres, commonly referred to as plasma balls. The laser exerts a nonlinear ponderomotive force on the cluster electrons, causing them to oscillate with a nonlinear velocity. This nonlinear motion leads to perturbations in the electron density within the cluster. Furthermore, the oscillatory velocity interacts with an externally applied wiggler magnetic field, giving rise to an additional ponderomotive force. This results in a nonlinear velocity component that contributes to the generation of a nonlinear current density at the second harmonic. As a consequence of this nonlinearity, second harmonic generation (SHG) is observed. To enhance its efficiency, various parameters are optimized. It is found that a q-Gaussian laser beam with a flattened top (characterized by the q parameter) leads to a broadened plasmon resonance, thereby improving the efficiency of harmonic generation. The anharmonicity of the clusters further enhances their nonlinear response. Additionally, the amplitude of the second harmonic increases under an external wiggler magnetic field and at higher laser intensity. The maximum normalized amplitude is obtained for q = 0.7 and a cluster radius of 10 nm.</p>