This study aims to identify differences in the functional neural connectivity of the brain of paediatric patients with obstructive sleep apnea. Using EEG signals from 3673 paediatric patients, we grouped subjects into OSA or control groups based on sleep oxygen desaturation levels and apnea-hypopnea index (AHI), and applied topological data analysis (TDA) techniques. We evaluated our approach through statistical testing of TDA-based EEG features, which indicate fundamental differences in the functional neural connectivity of subjects with sleep apnea as compared to controls. There were statistically significant differences (