Answer by Sumith Harshan for Exclude only first post from one category from the latest posts feed, wordpress

Method - 1

$cat_posts = new WP_Query('posts_per_page=1&cat=2'); //first 1 posts
while($cat_posts->have_posts()) { 
   $cat_posts->the_post(); 
   $do_not_duplicate[] = $post->ID;
}

//Then check this if exist in an array before display the posts as following.
 if (have_posts()) {
    while (have_posts()) {

    if (in_array($post->ID, $do_not_duplicate)) continue; // check if exist first post

     the_post_thumbnail('medium-thumb'); 

         the_title();

    } // end while
}

Method - 2

query_posts('posts_per_page=6&offset=1');
if ( have_posts() ) : while ( have_posts() ) : the_post();

This query is telling the loop to only display 5 posts which follow the most recent first post. The important part in this code is “offset” and this magic word is doing the whole thing.

More details from Here