Pediatric obstructive sleep apnea (OSA) is a prevalent disorder that disrupts sleep and is associated with neurocognitive and behavioral negative consequences, potentially hampering the development of children for years. However, its relationships with sleep electroencephalogram (EEG) have been scarcely investigated. Here, our main objective was to characterize the overnight EEG of OSA-affected children and its putative relationships with polysomnographic measures and cognitive functions. A two-step analysis involving 294 children (176 controls, 57% males, age range: 5–9 years) was conducted for this purpose. First, the activity and irregularity of overnight EEG spectrum were characterized in the typical frequency bands by means of relative spectral power and spectral entropy, respectively: δ1 (0.1–2 Hz), δ2 (2–4 Hz), θ (4–8 Hz), α (8–13 Hz), σ (10–16 Hz), β1 (13–19 Hz), β2 (19–30 Hz), and γ (30–70 Hz). Then, a correlation network analysis was conducted to evaluate relationships between them, six polysomnography variables (apnea–hypopnea index, respiratory arousal index, spontaneous arousal index, overnight minimum blood oxygen saturation, wake time after sleep onset, and sleep efficiency), and six cognitive scores (differential ability scales, Peabody picture vocabulary test, expressive vocabulary test, design copying, phonological processing, and tower test). We found that as the severity of the disease increases, OSA broadly affects sleep EEG to the point that the information from the different frequency bands becomes more similar, regardless of activity or irregularity. EEG activity and irregularity information from the most severely affected children were significantly associated with polysomnographic variables, which were coherent with both micro and macro sleep disruptions. We hypothesize that the EEG changes caused by OSA could be related to the occurrence of respiratory-related arousals, as well as thalamic inhibition in the slow oscillation generation due to increases in arousal levels aimed at recovery from respiratory events. Furthermore, relationships between sleep EEG and cognitive scores emerged regarding language, visual–spatial processing, and executive function with pronounced associations found with EEG irregularity in δ1 (Peabody picture vocabulary test and expressive vocabulary test maximum absolute correlations 0.61 and 0.54) and β2 (phonological processing, 0.74; design copying, 0.65; and Tow 0.52). Our results show that overnight EEG informs both sleep alterations and cognitive effects of pediatric OSA. Moreover, EEG irregularity provides new information that complements and expands the classic EEG activity analysis. These findings lay the foundation for the use of sleep EEG to assess cognitive changes in pediatric OSA.