Not sure if this is what you are looking for:
Published on <a class="entry-date" href="https://wordpress.stackexchange.com/questions/326851/<?php echo
get_month_link(get_post_time("Y'),get_post_time('m')); ?>" >
<span itemprop="datePublished"><?php echo the_modified_date('F j, Y'); ?>
</span></a>
This will replace the published date by the last modified
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