Is there any manga (...)?

no

http://www.mangago.me/read-manga/game_over_mizutani_fuka/
Skip the first three one shots. The main story starts after them.

http://www.mangago.me/read-manga/gokusen/

http://www.mangago.me/read-manga/ai_to_ao_no_kyoukai/ - He's 19, so technically an adult, but she is 10 years older.

http://www.mangago.me/read-manga/four_years_apart/

http://www.mangago.me/read-manga/i_m_only_14_but_i_ll_make_you_happy/

This one is a highschooler and an elementary schooler http://www.mangago.me/read-manga/please_save_my_earth/
There's a sequel where they're older so ya eventually it's an adult with a school kid