Do you know what those terms you gave mean? A class 3 refers to a person with an underbite. Since you said your son has "maxillary deficiency" that means his top jaw (also known as the maxilla) has not grown enough in comparison with his bottom jaw (the mandible). Thus, his bottom jaw jets out and causes the bottom teeth to lie in front of the top teeth. You probably knew that just by looking at his bite!
I'm not an expert on this, but I have learned some about this condition while searching for information online about my problem "class 2" (overbite). Many sources I have come across that give information about class 2, also discuss the class 3 so I have read about it as well. Also, two of my cousins, both are brothers, have the class 3. I haven't talked with them in detail about this, so I don't know if they have maxillary deficiency, like your son, or if they had mandibular excess, or both conditions.
I do know age plays a part in treatment. Since you didn't give your son's age, I can't exactly say what his treatment might entail. I do know my older cousin, had to have surgery to fix his underbite because he was either finished growing, or almost finished growing. (He had the surgery in June, and he is 18.) His brother, who is 9, will be able to avoid surgery with appliances to control the way his jaws will grow. I think headgear is customary. I'm not exactly sure. Search online for more information. I usually am hesitant to take websites very seriously, but I have come across dozens of websites about jaw and teeth problems, and they have been really helpful. Good luck!