"On a page" or "in a page" for a web page

Either is (or even both are) correct, but the preposition changes the meaning.

John Lawler's answer here goes some way to explaining the difference: the choice of preposition distinguishes between the surface and the container.

If you are treating the web page as similar to a book page — a fairly transparent metaphor — then one would use on because you are referring to something printed/written on the surface of the page. It's unlikely that you are referring to something in the physical structure of the page.

It's on page 474 of this book.
It's on the front page of the website.

However, because web pages are usually built from structured code, it's quite easy to find something in the physical structure of the page. In this case, you're not concerned about what appears on the screen ( = the surface of the page), you're concerned with how the screen appears how it does. This could be applied to a book page, but it's less likely that something will happen within the actual paper.

There's malicious code in that page.
I found a spider squashed in the page of the book.