How to Register and Display Widget for Custom taxonomy

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There’s at least 3 options:

  1. You could take the code for the native recent posts widget and
    modify it in your child theme to work with your custom taxonomy.
  2. You could create a new WP_Query using the tax parameters.
  3. Or you could use a filter widget_posts_args to modify the default output of the native recent posts widget so it outputs your custom taxonomy.

I suggest you look into the core and find the native recent posts widget or category widget and take a look at the code. Try wp-includes/default-widgets.php.