WordPress Pagination with Get Value

You can create your custom pagination using paginate_link() function and add custom query string after current url.

To add argument to the links of paginations you can pass them as array argument inside the ‘add_args’

if ( is_home() || is_archive() || is_search() ) : 

    echo paginate_links(array(
         'base' => preg_replace('/\?.*/', "https://wordpress.stackexchange.com/", get_pagenum_link(1)) . '%_%',
         'current' => max(1, get_query_var('paged')),
         'format' => 'page/%#%',
         'total' => $wp_query->max_num_pages,
         // here you can pass custom query string to the pagination url
         'add_args' => array(
             'sort_by_type' => ( !empty($_GET['sort_by_type']) ) ? $_GET['sort_by_type'] : 'vote'
         )
     ));    

endif; 

Replace your pagination code with this above code.

It will print all string with custom query string.
http://example.com/page/2/?sort_by_type=vote

Hope this help!