This study proposes a novel lightweight neural network model leveraging features extracted from electrocardiogram (ECG) and respiratory signals for early OSA screening. ECG signals are used to generate feature spectrograms to predict sleep stages, while respiratory signals are employed to detect sleep-related breathing abnormalities. By integrating these predictions, the method calculates the apnea-hypopnea index (AHI) with enhanced accuracy, facilitating precise OSA diagnosis. The method was validated on three publicly available sleep apnea databases: the Apnea-ECG database, the UCDDB dataset, and the MIT-BIH Polysomnographic database. Results showed an overall OSA detection accuracy of 0.978, highlighting the model's robustness. Respiratory event classification achieved an accuracy of 0.969 and an area under the receiver operating characteristic curve (ROC-AUC) of 0.98. For sleep stage classification, in UCDDB dataset, the ROC-AUC exceeded 0.85 across all stages, with recall for Sleep reaching 0.906 and specificity for REM and Wake states at 0.956 and 0.937, respectively. This study underscores the potential of integrating lightweight neural networks with multi-signal analysis for accurate, portable, and cost-effective OSA screening, paving the way for broader adoption in home-based and wearable health monitoring systems.