The Japanese did invade part of Alaska -- the small islands of Attu and Kiska. These older threads go into the "why" of doing so.

https://www.reddit.com/r/AskHistorians/comments/6biipf/what_was_the_strategic_value_of_the_aleutians_to/

https://www.reddit.com/r/AskHistorians/comments/7eezzt/why_didnt_the_us_use_the_aleutian_islands_against/

https://www.reddit.com/r/AskHistorians/comments/80xu8w/did_the_japanese_seriously_consider_invading/duzfrpa/