Adding the time to the date on the blog index is a little tricker, since it’s done via a function. Here are the steps:
1) Add this to your child theme’s functions.php file. If your child theme already has a functions.php file, omit the opening <?php tag and just add everything else.
<?php
function dusktodawn_posted_on_with_time() {
printf( __( '<a href="%1$s" title="%2$s" rel="bookmark"><time class="entry-date" datetime="%3$s" pubdate>%4$s</time></a> at <span class="time">%2$s </span><span class="byline"> <span class="sep"> by </span> <span class="author vcard"><a class="url fn n" href="%5$s" title="%6$s" rel="author">%7$s</a></span></span>', 'dusktodawn' ),
esc_url( get_permalink() ),
esc_attr( get_the_time() ),
esc_attr( get_the_date( 'c' ) ),
esc_html( get_the_date() ),
esc_url( get_author_posts_url( get_the_author_meta( 'ID' ) ) ),
esc_attr( sprintf( __( 'View all posts by %s', 'dusktodawn' ), get_the_author() ) ),
esc_html( get_the_author() )
);
}
2) Create a copy of content.php from your parent theme and place it in the child folder. Change this line:
<?php dusktodawn_posted_on(); ?>
to this, to call in your newly modified function which displays the time:
<?php dusktodawn_posted_on_with_time(); ?>
This is what it looks like on a standard post:
Note that the time will also be added to the date on single posts as well, because they both use the same function.
Edit: I change the word “on” to “at” in the function as that makes more sense with the time.