How to highlight or show new to the particular posts list

Question

Ok, to display the latest posts you use default Recent Posts widget.

You can see it here: Appearance -> Widgets

This widget has no settings and is fine for getting started, you can install any plugin which will add a more sophisticated widget to your site, you just need to search for: Recent Posts Widget

I found the following:

And more…

Just go to plugins and add it to your site, then select it in widgets and customize accordingly

Edit

Change the post title relative to the date (if a month has not passed since the publication)

function wpb_lastvisit_the_title ( $title, $id ) {
    if ( is_singular() || get_post_type( $id ) != 'post' ) return $title;   

    $p = get_post( $id );
    $now = new DateTime();
    $date = DateTime::createFromFormat(get_option( 'date_format' ), $p->post_date);
    if($date){
        $interval = $now->diff($date);

        $days = $interval->d;
        // If a month has not passed, show the label
        if($days <= 30) {
            $title .= ' <span class="new-article">New</span>';
        } 
    }
    return $title;
}

add_filter( 'the_title', 'wpb_lastvisit_the_title', 10, 2);

By tag:

function wpb_lastvisit_the_title ( $title, $id ) {
    if ( is_singular() || get_post_type( $id ) != 'post' ) return $title;

    $tag_ids = wp_get_post_tags($id, array('fields' => 'ids'));
    // tag with name - new
    $tagId = get_term_by('slug', 'new', 'post_tag') -> term_id;
  if(in_array($tagId, $tag_ids)) {
        $title .= ' <span class="new-article">New</span>';
    }
    return $title;
}

add_filter( 'the_title', 'wpb_lastvisit_the_title', 10, 2);