• Ages 5.0 to 17.9 years at the time of screening

• Children with OSA and obstructive apnea hypopnea index (OAHI) ≥5/hour.

• Absence of clinically significant hypoxia defined as oxygen saturation \<88% for 5 minutes or episodic desaturation to 60% as these levels would otherwise identify children eligible to routinely receive oxygen.

• Favorable response to oxygen therapy (allowing randomization) will be defined as follows:

‣ Oxygen saturation nadir \>92% and

⁃ Decrease in obstructive index \< 5 / hour or by \> 50% from screening PSG

⁃ Reaching an optimum oxygen flow which is defined as the flow that achieves the lowest level of AHI with maximum CO2 level less than 65 mmHg observed for 5 consecutive minutes and or an increase in CO2 by less than 15 points above baseline. The above criteria are observed while the patient spends a minimal of 30 minutes in the supine position and at least one cycle of rapid eye movement (REM) sleep.

⁃ Oxygen flow required does not exceed 3.0 LPM and does not exceed a FiO2 \> 40 %.

• Willingness to comply with all study procedures and available for duration of study.

• At baseline the participant attempts to perform the neuropsychological tests