As a cornerstone technique for autonomous driving, Bird's Eye View (BEV) segmentation has recently achieved remarkable progress with pinhole cameras. However, it is non-trivial to extend the existing methods to fisheye cameras with severe geometric distortion, ambiguous multi-view correspondences and unstable temporal dynamics, all of which significantly degrade BEV performance. To address these challenges, we propose FishBEV, a novel BEV segmentation framework specifically tailored for fisheye cameras. This framework introduces three complementary innovations, including a Distortion-Resilient Multi-scale Extraction (DRME) backbone that learns robust features under distortion while preserving scale consistency, an Uncertainty-aware Spatial Cross-Attention (U-SCA) mechanism that leverages uncertainty estimation for reliable cross-view alignment, a Distance-aware Temporal Self-Attention (D-TSA) module that adaptively balances near field details and far field context to ensure temporal coherence. Extensive experiments on the Synwoodscapes dataset demonstrate that FishBEV consistently outperforms SOTA baselines, regarding the performance evaluation of FishBEV on the surround-view fisheye BEV segmentation tasks.