...

I can't think of any where a student is a dad, but there are a couple where a student has to take care of his sibling, or a sibling's child.

http://www.mangago.zone/read-manga/path_to_you/ (university student helping to look after his little brother (kindergarten age))

http://www.mangago.zone/read-manga/the_wolf_in_the_flower_shop/ (high school student helping to look after his younger brother (primary school age))

http://www.mangago.zone/read-manga/dekichatta_danshi/ (high school student has to look after a baby after the sister dumps the baby on him)

http://www.mangago.zone/read-manga/we_only_held_hands/