Xiaobaitu, please advise. 中华人民共和国国籍法，父母是中国公民的

Thanks Xiaobaitu. I'd like you to advise me what I should do.
My son was born in US and he went back to China with US passport/Traval certificate. Two years later, when I left China with F1, I was told he needed a Chinese passport in order to exit China, I did for his and applied F2 visa for him. after entering the US, we have travelled with his US possport. I wonder if you can tell me if he has trouble traveling between China and US, and how I can maintain his US citizenship. Thanks a lot.