Amend theme php to include certain category in header

You can use the action pre_get_posts. It gets fired after the query object is created but before the query is run.

This is an example from the official documentary for displaying only one category:

In your functions.php add the following:

function my_home_category( $query ) {
    if ( $query->is_home() && $query->is_main_query() ) {
        $query->set( 'cat', '123' );
    }
}

add_action( 'pre_get_posts', 'my_home_category' );