How to limit search to first letter of title?

I know it is too late but I hope it is going to help someone in the future
You can add a filter to posts_where and add a regexp to limit it to the first letter. WordPress documentation for posts_where

add_filter( 'posts_where' , 'posts_where' );

function posts_where( $where ) {

if( is_admin() ) {
    global $wpdb;

    if ( isset( $_GET['author_restrict_posts'] ) && !empty( $_GET['author_restrict_posts'] ) && intval( $_GET['author_restrict_posts'] ) != 0 ) {
        $author = intval( $_GET['author_restrict_posts'] );

        $where .= " AND ID IN (SELECT object_id FROM {$wpdb->term_relationships} WHERE term_taxonomy_id=$author )";
    }
}
return $where;
}