Next, we will add our class. So we need to find where ul starts:

  <ul>
<?php 
  $cat_args['title_li'] = '';
  
  /**
   * Filter the arguments for the Categories widget.
   *
   * @since 2.8.0
   *
   * @param array $cat_args An array of Categories widget options.
   */
  wp_list_categories( apply_filters( 
    ' widget_categories_args', $cat_args));

In this line, we will add class="w3-ul":

<ul class="w3-ul">

Now, reload the frontend page, and now it looks like it did before as shown in the following screenshot: