Multimodal emotion recognition in conversations is inherently challenging due to ambiguous cues, modality conflicts, and temporal dynamics, all of which contribute to complex and diverse uncertainty sources. While some recent methods incorporate uncertainty modeling, they often focus on overall prediction confidence, without explicitly distinguishing the different sources of uncertainty introduced by underlying factors. To address these challenges, we propose a novel Emotion-Specific Evidence Decomposition framework (ESED) that leverages evidential deep learning to explicitly model and disentangle multimodal emotional uncertainty. Rather than directly fusing features, ESED decomposes each modality's evidence into three interpretable components: (1) emotion-consistent evidence, capturing shared emotional cues across modalities; (2) emotion-specific evidence, highlighting the unique emotional role of each modality; and (3) dynamic evidence, modeling utterance-level temporal variations. These components are adaptively weighted based on emotional intensity, ambiguity, and dynamicity, quantified via prediction entropy, inter-modal divergence, and temporal variance. The final prediction is obtained through an adaptive fusion of these weighted components. Extensive experiments demonstrate that ESED outperforms the state-of-the-art methods on the MELD and IEMOCAP datasets, demonstrating the effectiveness of our proposed method.