Files are said to reside on a hard drive or on a certain machine. Since I know that a website is made of computer files, I think of a website as being on a machine and so any part of the website is also on that machine.
A website's "address" is a "Uniform Resource Locator" or URL. These terms connote the idea of website as "place". In this case the file would be at the website location.
So, if you think of a website as it is actually constructed (files stored on hard drives), you will probably say on.
If you think in the location metaphor, you will probably say at.
Link to an answer for a related ELU question