There is a note on the door and on it is written that

Question

What's the right way to say that? I mean I have a note and I have some kind of text on it, and I want to combine these sentences.

Answer 1

It's fine. Grammatically there is an ambiguity, but once you've mentioned a note, anyone not being deliberately perverse will understand that the message is written on the note and not on the door.

Answer 2

Even though the note can not speak, we often write, there is a note on the door which says...

Or, the note on the door indicates that...

Answer 3

There is a note on the door saying "..."

In the quotation marks, you could report the exact words the note says.