Vector beams with customizable topological charges hold significant potential for augmenting the capacity of optical communication systems. However, their propagation through random media like atmospheric turbulence induces wavefront distortion and intensity scintillation, severely degrading performance. To address this, we propose and design an inverse super-Gaussian non-uniformly correlated vector beam (ISGNCVB) with a tunable coherence structure. We thoroughly investigate its propagation characteristics in turbulent conditions. Our results demonstrate that the non-uniform correlation design confers remarkable self-focusing effects and stabilizes the received intensity profile. This leads to a signal-to-noise ratio (SNR) gain of up to 2 dB compared to its uniformly correlated counterpart. Furthermore, the polarization mode purity of the ISGNCVB exhibits enhanced robustness against turbulence-induced degradation. These advantages make the ISGNCVB a highly promising candidate for high-performance free-space optical communication links.