1. He watched some videos at the CNN website.

2. He watched some videos in the CNN website.

3. He watched some videos on the CNN website.

Which preposition is correct?

2 answers

The last one is the standard idiom.
Number 3 is the most common usage. Some prepositions have such vague or multiple meanings that the "correct" preposition is more a matter of custom than of any specific wrong or right.