The A6M2-N came to be as a result of the Japanese Navy issuing a spec for a single-seat fighter seaplane to provide air cover during the early phases of amphibious landing operations, and to fulfill the same role for military installations on small islands where building airstrips was not practical.
Kawanishi began work on the N1K1 Shiden, but it would not be ready in time for the impending conflict with the USA. The Navy then instructed Nakajima to develop a seaplane fighter based on the A6M2 which was then being built under license from Mitsubishi.
If I recall correctly Nakajima built more A6M's than did Mitsubishi, including a good number of A6M2 Model 11 airframes. It was an A6M2 Model 11 which was modified to serve as the prototype for the new seaplane fighter. There were 327 'Rufes' built, all by Nakajima.
As to the 'N' suffix... it probably was a special-function designator, as evangilder stated. What it meant, specifically, I wouldn't know; meatballs ain't my thing...
Fade to Black...