In Heterogeneous Distributed Systems (HDS), efficient task scheduling (TS) across diverse resources remains a pressing challenge. This paper introduces a Hybrid Genetic Algorithm (HGA) as a solution, blending heuristic techniques with the evolutionary strengths of Genetic Algorithms (GAs) to optimize Task Scheduling (TS). Traditional algorithms often fall short in balancing computational speed with solution quality, especially in large-scale environments. This proposed HGA addresses this by leveraging domain-specific heuristics to provide a promising starting point for the GA's optimization process. The TS dilemma has been successfully defined by an all-encompassing logical system, which ensures the accuracy of the design of algorithms. In comparison tests, the HGA frequently comes out on top, demonstrating less makespan and a more excellent distribution of tasks among the resources available. Also, resources with more efficient processing capabilities will be provided priority in this recommended heuristic method, which focuses on tasks with higher computational demands. The findings of the present investigation demonstrate that the HGA may transform TS approaches by providing high-quality solutions while increasing performance.