I’m not really sure what you’re asking. The author of a post and the date are already in Twenty Fifteen.
The file you’re looking for is wp-content/themes/twentyfifteen/content.php, where on line 56 you’ll see the following code:
<?php twentyfifteen_entry_meta(); ?>
That code calls the twentyfifteen_entry_meta function from wp-content/themes/twentyfifteen/inc/template-tags.php, which creates the HTML for the entry meta. If you’re dealing with a post, not a page, and the post is singular (i.e., you’ve clicked through to a single post) or you’re dealing with a multi-author blog, the author’s name is displayed.
Since the developer has considerately added the:
if ( ! function_exists( 'twentyfifteen_entry_meta' ) ) :
you should be able to override the built-in function by adding one to your child theme’s functions.php and output whatever you want.