“New” next to the post title

you could use some code like this:

<?php if( (time() - get_the_time('U')) < (24*60*60) ) { echo 'new '; }; ?>

the numbers above are for: 24 hours * 60 minutes * 60 seconds

https://uk2.php.net/manual/en/function.time.php
https://codex.www.ads-software.com/Function_Reference/get_the_time
https://uk2.php.net/manual/en/function.date.php

So do I put this code next to the title function?

Actually where do I put that code? Can I also use it for displaying the word “new” next to category?

this is the post title line from the default theme’s index.php:
<h2><a href="<?php the_permalink() ?>" rel="bookmark" title="Permanent Link to <?php the_title_attribute(); ?>"><?php the_title(); ?></a></h2>

you could add the code like this:
<h2><?php if( (time() - get_the_time('U')) < (24*60*60) ) { echo 'new '; }; ?><a href="<?php the_permalink() ?>" rel="bookmark" title="Permanent Link to <?php the_title_attribute(); ?>"><?php the_title(); ?></a></h2>

the ‘new’ would appear in the same line as the title, but not linked.

Can I also use it for displaying the word “new” next to category?

as long as it is in the loop, you could put that code anywhere; just be aware the the term ‘new’ refers to the creation date of the post.

alchymyth thank you very much for your useful information