Leading zeros are not allowed in Python?

Finally, I got my answer. Below is the working code.

def permute_string(str):
    if len(str) == 0:
        return ['']
    prev_list = permute_string(str[1:len(str)])
    next_list = []
    for i in range(0,len(prev_list)):
        for j in range(0,len(str)):
            new_str = prev_list[i][0:j]+str[0]+prev_list[i][j:len(str)-1]
            if new_str not in next_list:
                next_list.append(new_str)
    return next_list

#Number should not be with leading Zero
actual_list = '129, 831 ,054, 845,376,970,074,345,175,965,068,287,164,230,250,983,064'
list = actual_list.split(',')
length = len(list)
i = 0

# Iterating using while loop
while i < length:
    a = list[i]
    print(permute_string(str(a)))
    i += 1;

Integer literals starting with 0 are illegal in python (other than zero itself, obviously), because of ambiguity. An integer literal starting with 0 has the following character which determines what number system it falls into: 0x for hex, 0o for octal, 0b for binary.

As for the integers themselves, they're just numbers, and numbers will never begin with zero. If you have an integer represented as a string, and it happens to have a leading zero, then it'll get ignored when you turn it into an integer:

>>> print(int('014'))
14

Given what you're trying to do here, I'd just rewrite the list's initial definition:

lst = ['129', '831', '014']
...
while i < length:
    a = lst[i]
    print(permute_string(a))  # a is already a string, so no need to cast to str()

or, if you need lst to be a list of integers, specifically, then you can change how you convert them to strings by using a format-string literal, instead of the str() call, which allows you to pad the number with zeros:

lst = [129, 831, 14]
...
while i < length:
    a = lst[i]
    print(permute_string(f'{a:03}'))  # three characters wide, add leading 0 if necessary

---

throughout this answer, I use lst as the variable name, instead of the list in your question. You shouldn't use list as a variable name, because it's also the keyword that represents the built-in list datastructure, and if you name a variable that then you can no longer use the keyword.