Pulse rate variability (PRV), an alternative measure of heart rate variability (HRV), is altered during obstructive sleep apnea. Correntropy spectral density (CSD) is a novel spectral analysis that includes nonlinear information. We recruited 160 children and recorded SpO2 and photoplethysmography (PPG), alongside standard polysomnography. PPG signals were divided into 1-min epochs and apnea/hypoapnea (A/H) epochs labeled. CSD was applied to the pulse-to-pulse interval time series (PPIs) and five features extracted: the total spectral power (TP: 0.01–0.6 Hz), the power in the very low frequency band (VLF: 0.01–0.04 Hz), the normalized power in the low and high frequency bands (LFn: 0.04–0.15 Hz, HFn: 0.15–0.6 Hz), and the LF/HF ratio. Nonlinearity was assessed with the surrogate data technique. Multivariate logistic regression models were developed for CSD and power spectral density (PSD) analysis to detect epochs with A/H events. The CSD-based features and model identified epochs with and without A/H events more accurately relative to PSD-based analysis (area under the curve (AUC) 0.72 vs. 0.67) due to the nonlinearity of the data. In conclusion, CSD-based PRV analysis provided enhanced performance in detecting A/H epochs, however, a combination with overnight SpO2 analysis is suggested for optimal results.