How to add a post filter by category above the post blocks in the archive?

Question

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Hello dear community! Please help me add an AJAX post filter by category above the post blocks in the archive on the wordpress site. The theme is Kadence. It is necessary that there be a drop-down list under the name of the page of the archive of records and when you go to the heading, the entries from this heading are shown automatically. The default theme archive page should be used. I want to do it the way it is on the site https://design-davydova.ru/blog/
But there it is already implemented in the theme itself. I did not manage to get and redo the code. I beg you to help!

Answer 1

Has no one filtered posts in wordpress? Maybe a plugin then tell me? I just don’t want a separate page with a shortcode output, I need to insert something into archive.php to be shown on the standard archives page