Graph Convolutional Networks (GCNs) have proven to be highly effective for skeleton-based action recognition, primarily due to their ability to leverage graph topology for feature aggregation, a key factor in extracting meaningful representations. However, despite their success, GCNs often struggle to effectively distinguish between ambiguous actions, revealing limitations in the representation of learned topological and spatial features. To address this challenge, we propose a novel approach, Gaussian Topology Refinement Gated Graph Convolution (G$^{3}$CN), to address the challenge of distinguishing ambiguous actions in skeleton-based action recognition. G$^{3}$CN incorporates a Gaussian filter to refine the skeleton topology graph, improving the representation of ambiguous actions. Additionally, Gated Recurrent Units (GRUs) are integrated into the GCN framework to enhance information propagation between skeleton points. Our method shows strong generalization across various GCN backbones. Extensive experiments on NTU RGB+D, NTU RGB+D 120, and NW-UCLA benchmarks demonstrate that G$^{3}$CN effectively improves action recognition, particularly for ambiguous samples.