How to Query in WordPress which shows Alphabetic Posts?

Assuming the letters are links, then put the letter into the URL as a parameter. E.g.:

http://example.com/brands/?letter=N

Then, in the code (inside whichever template file will be used here), you need to query the DB for posts/brands beginning with ‘N’.

You can either create a taxonomy for letters (https://codex.wordpress.org/Function_Reference/register_taxonomy) and assign each post to a letter (where the taxonomy’s terms are all the letters`), and then use one of the following:

There are several ways:

1 – WP_Query

2 – get_posts()

.. Several other methods.

Here is how you can do it with WP_Query:

$args = array(
    'post_type' = 'brands', //assuming the post type slug is 'brands'
    'posts_per_page' = -1,
    'tax_query' => array(
        array(
            'taxonomy' => 'letters',
            'field'    => 'slug',
            'terms'    => 'N', // sanitize_text_field($_GET['letter'])
        ),
    ),
); 

$the_query = new WP_Query( $args );

if ( $the_query->have_posts() ) {

    while ( $the_query->have_posts() ) {
        $the_query->the_post();
        the_title();
    }

    /* Restore original Post Data */
    wp_reset_postdata();
} else {
    echo 'no brands beginning with N;
}

Or, instead of having to create a taxonomy for letters, you could do this (a more-custom query, using $wpdb):

     global $wpdb; 
     $request = sanitize_text_field($_GET['letter']);
     $results = $wpdb->get_results(
            "
            SELECT * FROM $wpdb->posts
            WHERE post_title LIKE '$request%'
            AND post_type="brands"
            AND post_status="publish"; 
            "
     ); 
     if ( $results ) 
     {
        foreach ( $results as $post ) 
        {
            setup_postdata ( $post ); 
            the_title();
        }
     } 
     else 
     {
        echo 'no brands beginning with 'N';
     }

More on $wpdbhttps://codex.wordpress.org/Class_Reference/wpdb

More on WP_Queryhttps://codex.wordpress.org/Class_Reference/WP_Query