python3 NameError variable not defined

There is no global i. The variable you want is in the non-local enclosing scope.

class Solution:
    def kthSmallest(self, root: TreeNode, k: int) -> int:
        i = 0
        def inOrder(root):
            nonlocal i
            if root == None:
                return
            inOrder(root.left)
            i += 1
            if i == k:
                return
            inOrder(root.right)

        inOrder(root)
        return i

The scopes of kthSmallest and inOrder are different. Without specifying i as a global variable in kthSmallest, i won't be known inside inOrder.

Nested functions scopes

For nested functions, you need to declare your global variable in the parent function scope as well.

    class Solution:

        def kthSmallest(self, root: TreeNode, k: int) -> int:
            global i
            i = 0

            def inOrder(root):
                global i
                if root is None:
                    return
                inOrder(root.left)
                i += 1
                if i == k:
                    return
                inOrder(root.right)

            inOrder(root)
            return i

Remark 1

It looks like you are using a class in your example. You could also have done the following:

    class Solution:
        self.i = 0
        def kthSmallest(self, root: TreeNode, k: int) -> int:
            self.i = 0 

            def inOrder(root):
                if root is None:
                    return
                inOrder(root.left)
                self.i += 1
                if self.i == k:
                    return
                inOrder(root.right)

            inOrder(root)
            return i