The three generation is the third generation. Depending on the context, you can sometimes use this alone to say you're third generation Japanese. Usually, though, you'll want to specify whether you're third generation Japanese or another nationality.
This is a jukugo word, which usually means on'yomi readings from the kanji. If you know the readings of your kanji you'll know how to read this as well.
the identity of the third generation
most of the third generation
Charles III has become the King of England.
My father is a third-generation Japanese born in the United States.
I take pride in being the third generation.