how to install second website on subfolder

So what server softare are you using? Apache, Nginx etc
Here's examples on Apache, as it's normally what people use.

Code:

<IfModule mod_rewrite.c>
   RewriteEngine on
   RewriteBase /onyx/
   RewriteCond %{REQUEST_FILENAME} !-f
   RewriteCond %{REQUEST_FILENAME} !-d
   RewriteRule ^(.*)$ /onyx/index.php/$1 [L,QSA]
</IfModule>

Code:

<IfModule mod_rewrite.c>
   RewriteEngine on
   RewriteBase /onyx/
   RewriteCond %{REQUEST_FILENAME} !-f
   RewriteCond %{REQUEST_FILENAME} !-d
   RewriteRule ^(.*)$ index.php/$1 [L,QSA]
</IfModule>