Upvote:3
Unlike US, Russia is not a Jus soli but a Jus sanguinis state.
That means if at least one of the parents is not a Russian citizen then a child got no rights to the Russian citizenship.
So your son is not a Russian citizen at all.
Also there is no such thing as exit visa in Russia, people (with exception of people working with classified info) can exit Russia freely (but they need an entry visa from the state they're headed into).
For children you should have either both parents present or a written consent of another parent to cross the border (and some evidence you're actually their parents).