Tried to keep using NestedList till the end since it was specifically mentioned, and came up with this. Feel free to point out errors, if any, and comment down if you have an optimized yet readable solution for the same.

`

if name == 'main':

studentlist = []
newlist = []
finallist = []

for _ in range(int(input())):
    name = input()
    score = float(input())
    studentlist.append([name, score])

# Sorting student's score in ascending order    
studentlist.sort(key=lambda x: x[1])

# Adding student's score which are higher than minimum score to a newlist 
for i in studentlist:
    if i[1] != studentlist[0][1]:
        newlist.append(i)

# Adding all the student's of newlist with the lowest score to the finallist            
for i in newlist:
    if i[1] == newlist[0][1]:
        finallist.append(i)       

# Sorting student's name alphabetically in the final list
finallist.sort()

[print(x[0]) for x in finallist]