@sonatarhia Bingo for Princeton research. Every Ivy has a similar program. Just explore/call to find out and apply. Very competitive though, will need strong support from HS science department. If unable to secure through this path, figure out areas of interest/choose something atypical, find out faculty at university doing that, and write to them (student should be doing all the communications)
Math+4: Calc in 9th grade. All courses done at HS, last yr independent study with faculty.
See this and explore that forum: High school math acceleration thread