Internet of Things (IoT) enabled wearable sensors for health monitoring are widely used to reduce the cost of personal healthcare and improve quality of life. The sleep apnea-hypopnea syndrome, characterized by the abnormal reduction or pause in breathing, greatly affects the quality of sleep of an individual. This paper introduces a novel method for apnea detection (pause in breathing) from electrocardiogram (ECG) signals obtained from wearable devices. The novelty stems from the high resolution of apnea detection on a second-by-second basis, and this is achieved using a 1-dimensional convolutional neural network for feature extraction and detection of sleep apnea events. The proposed method exhibits an accuracy of 99.56% and a sensitivity of 96.05%. This model outperforms several lower resolution state-of-the-art apnea detection methods. The complexity of the proposed model is analyzed. We also analyze the feasibility of model pruning and binarization to reduce the resource requirements on a wearable IoT device. The pruned model with 80\% sparsity exhibited an accuracy of 97.34% and a sensitivity of 86.48%. The binarized model exhibited an accuracy of 75.59% and sensitivity of 63.23%. The performance of low complexity patient-specific models derived from the generic model is also studied to analyze the feasibility of retraining existing models to fit patient-specific requirements. The patient-specific models on average exhibited an accuracy of 97.79% and sensitivity of 92.23%. The source code for this work is made publicly available.