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Deep learning has improved automated electrocardiogram (ECG) classification, but limited insight into prediction reliability hinders its use in safety-critical settings. This paper proposes UCTECG-Net, an uncertainty-aware hybrid architecture that combines one-dimensional convolutions and Transformer encoders to process raw ECG signals and their spectrograms jointly. Evaluated on the MIT-BIH Arrhythmia and PTB Diagnostic datasets, UCTECG-Net outperforms LSTM, CNN1D, and Transformer baselines in terms of accuracy, precision, recall and F1 score, achieving up to 98.58% accuracy on MIT-BIH and 99.14% on PTB. To assess predictive reliability, we integrate three uncertainty quantification methods (Monte Carlo Dropout, Deep Ensembles, and Ensemble Monte Carlo Dropout) into all models and analyze their behavior using an uncertainty-aware confusion matrix and derived metrics. The results show that UCTECG-Net, particularly with Ensemble or EMCD, provides more reliable and better-aligned uncertainty estimates than competing architectures, offering a stronger basis for risk-aware ECG decision support.