Third Generation
The three generation is the third generation. You can use this alone to say you're third generation Japanese or you can specify and say you're third generation something else.
さんせい
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.
ルイ三世は、フランスのきぞくです。
Louis III was a French noble.
ざい日三世のほとんどはかんこくごがはなせません。
Most of the third generation Koreans residing in Japan cannot speak Korean.
僕はアニメルパン三世を毎日見ます。
I watch the anime "Lupin the Third" every day.