wordpress in subdirectory

Hello,
My wordpress is installed in /home/user/wordpress
In my httpd.conf I added Alias /blog /home/user/wordpress
When I load https://site.com/blog all is fine, and wordpress work like a charm.The problem is when I try to access some of the pages.Mozilla give me error msg:

Firefox can’t find the server at site.comsite.comblog.

This is with settings:

WordPress address (URL): https://site.com/blog
Site address (URL): https://site.com/blog

If I change it to:

WordPress address (URL): https://site.com/blog
Site address (URL): https://site.com

I can not access my HOME blog page, from the link “HOME”

P.S. I have index.php in https://site.com that I want to use/save and make some link – blog, which will follow to the blog page.
Thanks