I have read all of them and they all tell the same thing. The Prime Minster of India. But then, which one is better to use. To me, grammatically, all mean different!
India Prime Minister -what sort of sentence structure is that? Something like America Farmer!
Indian Prime Minister -This talks more about the nationality of the prime minister or character of a person from a particular region. Something like What is the difference between Indian Prime Minister and Japanese Prime Minister. The latter one would have small eyes!
India's Prime Minister - fits better (in my opinion though).
What is your take on these?