Problems hosting WordPress in /blog alongside CodeIgniter 3 Application.

You need to change your .htaccess to exclude that url.

Code:

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