I have reformatted your code to display the post date and updated date with conditional. Also I have added correct link for the published date and also updated date. Please check following.
function chicken_wings_posted_on() {
$u_time = get_the_time('U');
$u_modified_time = get_the_modified_time('U');
if ($u_modified_time >= $u_time + 86400) {
echo '<p class="last-updated-up">Last updated on ';
echo '<a href="' . esc_url( get_day_link( get_the_modified_time( 'Y' ), get_the_modified_time( 'm' ), get_the_modified_time( 'd' ) ) ) . '">';
the_modified_time('F jS, Y');
echo '</a>';
echo "</p> ";
} else {
echo '<p class="entry-date published">Published on ';
echo '<a href="' . esc_url( get_day_link( false, false, false ) ) . '">';
the_time('F jS, Y');
echo '</a>';
echo "</p> ";
}
}