Hello,
To exclude a category from the ‘More posts’ section you need to modify the query by which it’s being formed in single.php (the $args array around line 62). Here are the possible category parameters described in the Codex.
So, for instance, to exclude a category with the id of 20 you would do the following:
$args = array(
'post_type' => 'post',
'post__not_in' => array(get_the_ID()),
'posts_per_page' => 2,
'category__not_in' => array( 20 ),
);
Please mind that it’s best to perform such modifications in a child theme, so that they do not get overwritten during a theme update.