It has to deal with the way verb phrases change when you have a question, as opposed to a statement. Let's look at a few examples:
What is the problem?
I don't know what the problem is.
Who are these people?
My mother wonders who these people are.
What these examples show is that in a sentence that's a statement (not a question), words like "who", "what" aren't directly followed by a verb like they are in a question.
So let's try to work backwards from your second example, and see what the corresponding question would look like.
- Statement: "I don't know which one correct is."
- Question: we move the verb after 'which', and we get "Which is one correct?". That's not a valid English sentence, so there was a problem with our statement too.
There are two ways to ask that question:
Version 1: "Which is the correct one?"
Explanation: we start with "which is", and that looks like our familiar pattern of question word followed by a verb. The corresponding statement then looks like "I don't know which the correct one is", after we move the verb 'is' to the end. That's a valid statement.
Version 2: "Which one is correct?" (or "Which one is the correct one?")
Explanation: the question word 'which' doesn't have a verb right after it. In that case, the word order in the corresponding statement doesn't change. We get "I don't know which one is correct."