“About a lung function sleep study?”

In regards to sleep apnea, I'm struggling to get a diagnosis for my son. He has sleep apnea not very noisy he lets out a big sigh then pauses sometimes between 10-18 seconds and this will happen through the night. Some nights seem to be worse than others but it’s been like this for the last 3 years now. First, they said obstruction but when they took him to get his tonsils and adenoids out there was no obstruction. So they didn’t do it. He has a cardiac history and had OHS for interrupted aortic arch type b large vsd and narrowing of the main valve which is monitored sleep study. We did this at home with an oximeter which showed flat-like saturations. We had a sleep study on lung function in the hospital in the morning when they did his blood gas it had clotted. Could this mean anything to help us get the right answers and diagnosis?