I can't ID it, but personally, I don't think it is NSDAP-related.
Offhand, I can't think of a Nazi organization called "NSS" or "SSN" or "SNS".
The logo doesn't ring any bells either, and the very modern straight/angular style of the lettering just doesn't have that typical "Nazi aesthetic" look to me.
the badge is indeed National Socialist related.
It is a members badge for the (NSS) NS Schulerbund.
They are quite hard to find even though the pin is broken I would have it in my collection like a shot.
All the best
great forum !!