What is the ruling on saying: "By the Prophet," and "By this Ramadan," and so on?

Swearing by the right of the Prophet (peace be upon him), or by the right of Ramadan, and similar expressions, does not constitute a valid oath, because it is swearing by other than Allah. The Prophet's right is to be honored, obeyed, and supported, and Ramadan's right is to be fasted. An oath is not made valid by swearing by created beings.