An example of adding list case custom fields to your contact form and making them required.

require_dropdowns.js

<!-- HTML -->
<div class="form-group div-category">
  <label for="ticket_custom_category" class="control-label">Category ({{system.snippets.required}}):</label>
  {{ ticket_custom_category }}
</div>
<div class="form-group div-favorite-color">
  <label for="customer_custom_favorite_color" class="control-label">Favorite Color ({{system.snippets.required}}):</label>
  {{ customer_custom_favorite_color }}
</div>

<!-- JavaScript -->
<script>
$(document).ready(function () {
  /* The code below makes your default (top) value blank for each custom field, forcing the user to 
  select an option. This assumes your list custom fields' first option is something like "---", 
  "Please select an option", etc. */
  $(".form-group select").each(function() {
    $(this).find("option:first").val("");
    $(this).rules("add", { required:true, messages: { required: "Field is required." } });
  });
  
});
</script>