A custom post time function for WordPress that allows you to change the output for posts that are published today.

WP custom post time

/** 
 * custom post time function
 *
 * @uses global $post, get_the_time() and get_the_date()
 * @vars $d (for custom date formatting), $t (for custom time formatting)
 * @returns $my_post_time
 */
function my_post_time($d, $t) {
	global $post;
	
	if ( date('Yz') == get_the_time('Yz', $post->ID) ) {
		$my_post_time = 'today at ' . get_the_time($t, $post->ID);
	} else {
		$my_post_time = 'on ' . get_the_date($d, $post->ID);
	}
	
	echo $my_post_time;
}