I have to say that the order of two substrings with the same length is so unclear.
I failed in the test only because of the order.
There must be much more explaination about it.

unpublished (see issue below)

Don't let wikipedia describe the kata for you.

In a case of having "2 11", I'd prefer the output to be sorted by stable sort, but it's your choice.

Good idea, I did it.

So the items between the bounds are taken from the sorted array... Then the description is ambiguous.

Or even between the bounds numerically, not in the array...

yeah...

As mentioned above, find both bounds in the sorted array, then as an independant operation, filter all values from the original array between those two bounds.

Now it looks more like an issue. Changed Suggestion to Issue.

If there are duplicates on the bounds, you have to include all of the duplicated numbers in the sum. So in your example, 2 is the second and third smallest number, you have to include both 2's in the sum. I guess if you had a list that was just [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] with i = 1 and j = 5, you would have to sum the entire list.

Ah yeah, I had not seen ^^

Already wrote a suggestion below ;)

Also with

def partial_sum(array, i, j):
    array.sort()
    return 0

it throws

Unexpected exception raised

Traceback (most recent call last):
  File "/workspace/default/.venv/lib/python3.10/site-packages/codewars_test/test_framework.py", line 112, in wrapper
    func()
  File "/workspace/default/tests.py", line 54, in test_case
    test.assert_equals(solution.partial_sum(lst, a, b), solver(lst,a, b))
  File "/workspace/default/tests.py", line 27, in solver
    a_element = select(array, 0, len(array)-1, a)
  File "/workspace/default/tests.py", line 22, in select
    return select(array, p, q-1, i)
  File "/workspace/default/tests.py", line 22, in select
    return select(array, p, q-1, i)
  File "/workspace/default/tests.py", line 22, in select
    return select(array, p, q-1, i)
  [Previous line repeated 991 more times]
  File "/workspace/default/tests.py", line 17, in select
    q = partition(array, p, r)
  File "/workspace/default/tests.py", line 7, in partition
    for j in range(p, r):
RecursionError: maximum recursion depth exceeded in comparison

I know this has to be a duplicate to one kata that I cannot recall AGN.... (Might be myjinxin's... which is 6kyu with a much more storyline-related description !

(Will modify my comment to be an issue once I found it!

The user can modify the input, and make crash the tests:

Unexpected exception raised

Traceback (most recent call last):
  File "/workspace/default/.venv/lib/python3.10/site-packages/codewars_test/test_framework.py", line 112, in wrapper
    func()
  File "/workspace/default/tests.py", line 54, in test_case
    test.assert_equals(solution.partial_sum(lst, a, b), solver(lst,a, b))
  File "/workspace/default/tests.py", line 27, in solver
    a_element = select(array, 0, len(array)-1, a)
  File "/workspace/default/tests.py", line 17, in select
    q = partition(array, p, r)
  File "/workspace/default/tests.py", line 11, in partition
    array[i+1], array[r] = array[r], array[i+1]
IndexError: list index out of range

With a code just containing

def partial_sum(array, i, j):
    array.clear()
    return 0

Please pass a copy to the user.