Modify Link in excerpt

what theme is the site using?

is that ‘promotion’ done with a widget in the right column middle?

Sorry, meant to include the code:

<div id="globalcontent">
<?php
$featuredPosts = new WP_Query();
$featuredPosts->query('showposts=5&cat=8');
while ($featuredPosts->have_posts()) : $featuredPosts->the_post(); ?>
<h2 style="color:#FFFFFF; background:url(https://ahy4life.com/images/right_top_header.jpg) no-repeat left top;"><center><a href="promos.php"><?php the_title(); ?></a></center></h2>
<div>
<style type="text/css">

div a{
color:#FFFFFF;
}

</style>

<?php the_excerpt(); ?>

<?php endwhile; ?>
</div>
      </div>
      <div><img src="images/right_top_footer.jpg" alt="" /></div>
      <div style="background-color: #FFF;"></div>

[please review how to properly mark any posted code – https://codex.www.ads-software.com/Forum_Welcome#Posting_Code
the above code is partially broken/corrupted.]

the ‘continue reading’ link for the excerpt might have been done with a filter in functions.php of the theme;

see: https://codex.www.ads-software.com/Function_Reference/the_excerpt#Make_the_.22read_more.22_link_to_the_post

Thank you. Found the code below. What do I need to modify for the ‘promos’ category?

function twentyeleven_continue_reading_link() {
	return ' <a href="events.php">' . __( 'Continue reading <span class="meta-nav">&rarr;</span>', 'twentyeleven' ) . '</a>';
}

‘normally’, as you might have seen in the Codex example, the link is using the_permalink() instead of a hardcode relative link.

I don’t know right now how and if you can create an automatic post specific relative link using WordPress default functions;
try the forum search.