Jason's Partner is a scrapped, unnamed character originally planned to appear in Blaster Master 2. She would possibly have been Jason's girlfriend, and would have been rescued in the first stage. From that point onward, she would have stayed within Sophia and served as a spotter whenever Jason left the vehicle. It has never been specified why she was removed from the game.
Interestingly, despite her removal, the role of a spotter would ultimately be fulfilled in the series by Elfie in Blaster Master: Blasting Again, as well as Eve. Because of the adoption of the Worlds of Power novel as canon, Eve would have been retconned in Jason's Partner's role as she served a similar purpose.