Is there any Schema.org type that I should use on my category page of my WordPress blogsite for the blogposts that are listed in the category?
ItemList doesnt seem apropriate. Any other suggestions?
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If it is a list of items that have their own pages (like this), then Google does recommend ItemList with just the URLs marked up.
You could extend it with a name, description, additionalType etc.
It's probably more valuable (with Google) to make sure you mark up the BlogPosting pages correctly. It's a sub type of Article, so those rules apply:
Since you're using Wordpress, the best plugin you can use for this purpose is Schema (https://wordpress.org/plugins/schema/). This article is not good if your website has products or reviews but it's good for a Blogsite, so do try it. Just install, set it up and let the plug in do the rest for you.