Thanks anyway my friends 👍

I'm sorry but there is no way to do that

Thanks, but this is not what I was looking for. 

if a visitor clicks on an attachment, a notification window pops-pup on the top-right screen asking them to login or register.

Those links are sending the visitors to the Login and Register pages. 
On my site, I'm using a modal for the login and register, and fortunately, I don't have any control over the notification's links. I can't customize them, change them, or disable them in any way.

This is why I thought about creating a text message just below the attachment inside the post, with my own Login & Register links (that only visitors can see), and this way a visitor could see that they need to sign in or register in order to download the file, and hopefully they won't click on the attachment and they also won't see the Login and Register notification window!

Cheers.

I'll suggest you check out the wpForo "Admin note/message on Forum frontend" feature (Dashboard > Forums > Tools > Misc admin page). 

The Admin message will be displayed under the forum breadcrumb menu, above forum and topic titles. you can display the text for certain usergroups. 

I would like to create a text/message inside a post that only visitors can see - Is there a shortcode for that?

I attached an example.