Rapidly-exploring Random Tree (RRT) and its variants have become foundational in path-planning research, yet in complex three-dimensional off-road environments their uniform blind sampling and limited safety guarantees lead to slow convergence and force an unfavorable trade-off between path quality and traversal safety. To address these challenges, we introduce HS-APF-RRT*, a novel algorithm that fuses layered sampling, an enhanced Artificial Potential Field (APF), and a dynamic neighborhood-expansion mechanism. First, the workspace is hierarchically partitioned into macro, meso, and micro sampling layers, progressively biasing random samples toward safer, lower-energy regions. Second, we augment the traditional APF by incorporating a slope-dependent repulsive term, enabling stronger avoidance of steep obstacles. Third, a dynamic expansion strategy adaptively switches between 8 and 16 connected neighborhoods based on local obstacle density, striking an effective balance between search efficiency and collision-avoidance precision. In simulated off-road scenarios, HS-APF-RRT* is benchmarked against RRT*, Goal-Biased RRT*, and APF-RRT*, and demonstrates significantly faster convergence, lower path-energy consumption, and enhanced safety margins.