Yes. You don't need to apply for his citizenship; you just have to list him on your N-400 and make sure he is living with you in the US at the time of your naturalization (or living with you any time after naturalization, as long as he is still under 18). However, you would need to apply for proof of his citizenship, either a passport or N-600 or both.Do you mean he will automatically become citizen along with me.
all the listed children under 18 at time of your own naturalization would be automatically naturalized after they become 18 year old.
Citizenship:
Since I have a strong base in US when I apply for citizenship for myself can I apply for my son also along with me.
Does your son enroll in Selective Service? if not, Join now! Because he is below 25 yrs old.
I am not clear about selective service you are talking about? My son is eight years old.