AFAIK minor children have the same status as their parent(s).
Under the Agreement on the Free Movement of Persons (AFMP) 2, family members who
are nationals of a Member State of the European Union (EU) 3 or European Free Trade
Association (EFTA) 4 and who are allowed to enter Switzerland on the grounds of family
reunification may ask the Population Office of their canton of residence to be issued with a
residence permit (B permit) instead of a legitimation card 5 (for family members of locally
recruited staff members, see section 4.1). Family members who hold a permit are subject
to Swiss law and are not entitled to privileges or immunities
And your son was ‘allowed to enter Switzerland on the grounds of family
reunification’ ?
This sounds like a spouse joining their CdL partner here in Switzerland. Not dependant children migrating with their parents. (or being born here)
There was a thread a few months ago about a young adult who grew up here wanting to get a permit. I recall there was a way but …
Edited to add, here it is. https://www.englishforum.ch/permits-…-c-permit.html