add pagination to custom category posts

You can try below code for display page with pagination. I set 6 to posts_per_page which restrict to display 6 post per page at a time.

<?php
//build $args for fetch records...
$paged = ( get_query_var( 'paged' ) ) ? get_query_var( 'paged' ) : 1;
$args = array(
  'posts_per_page' => 6,//display post per page
  'paged'          => $paged,
  'cat'                      => 1
);

//Fetch and loop until records..
$my_query = new WP_Query($args);
while ($my_query->have_posts()):
    $my_query->the_post();
    $do_not_duplicate = $post->ID;?>
     <a href="https://wordpress.stackexchange.com/questions/239816/<?php the_permalink() ?>"><?php the_title(); ?></a></br>
<?php endwhile; ?>

<!--For display links-->
<?php next_posts_link(); ?>
<?php previous_posts_link(); ?>