How to display post lists in the same term with paging

Hi,

I hope someone can help me with this problem as i’ve been trying for days..
I cant get my paging works well inside single page (custom post)

I created a WP site with custom post type UI.

== Structure ==
Custom post type UI : mypost
Custom taxonomy: mycategory
Terms in “mycategory” : cat1

== What i wanna do ==
This’s the result i wanna have.

<div class=left>
<!-- All posts in the same term -->
<p>Post1</p>
<p>Post2</p>
<p>Post3</p>
</div>
<div class=right>
<!-- contents of the post when clicked -->
<p>the_contents() for Post1</p>
</div>

My URL is https://domain/cat1/post1-title
I created a single-cat1.php for this.

The_contents()for post1 is easy

<?php if(have_posts() ): while(have_posts()) : the_post(); ?>
<p><?php esc_html(the_content()); ?>
<?php endwhile; endif; ?>

BUT i cant get my left menu works well..

Method 1

<?php
$args = array(
    'post_type' => 'mypost',
    'post_per_page' => '2',
    'tax_query' => array(
        array(
            'taxonomy' => 'mycat',
            'field'    => 'slug',
            'terms'    => "cat1",
        )
    )
);
$loop = new WP_Query($args);
while($loop->have_posts()) : $loop->the_post();
?>
<p><a href="<?php the_permalink(); ?>"><?php the_title(); ?></a></p>
<?php endwhile; ?>
<?php wp_reset_query(); ?>

<p><?php previous_posts_link('PREV'); ?></p>
<p><?php next_posts_link('NEXT'); ?></p>

The previous_posts_link & next_posts_link shows nothing.

Method 2

<?php
$t = array_shift(get_the_terms($post->ID, 'mycat'));
$tposts = get_posts('post_type=mypost&posts_per_page=2&taxonomy=mycat&term=cat1');
foreach($tposts as $tp) :
?>
<p><a href="<?php echo get_permalink($tp->ID); ?>"><?php echo esc_html($tp->post_title); ?></a></p>
<?php endforeach; ?>

<p><?php previous_posts_link('PREV'); ?></p>
<p><?php next_posts_link('NEXT'); ?></p>

The PREV or NEXT link is supposed to be paging for the left menu (list of posts within same term).

Would appreciate if anyone could help.

Thank you.