How to add a custom views filter handler for a specific field?
This require a little effort so I will only put here the main parts and a reference to an article that I used to create a custom Views filter in Drupal 8.

First you need to declare the filter inside the hook_views_data_alter() implementation:

$data['node_field_data']['nodes_titles'] = array(
  'title' =&gt; t('Node titles'),
  'filter' =&gt; array(
    'title' =&gt; t('Node titles'),
    'help' =&gt; t('Specify a list of titles a node can have.'),
    'field' =&gt; 'title',
    'id' =&gt; 'd8views_node_titles'
  ),
)


Since we are filtering on the title column, we are extending on the node_field_data table but with the title column as the real field to be used. Additionally, this time we are creating a plugin to handle the filtering identified as d8views_node_titles. Now it follows to create this class:

src/Plugin/views/filter/NodeTitles.php:
    

    /**
     * @file
     * Definition of Drupal\d8views\Plugin\views\filter\NodeTitles.
     */

    namespace Drupal\d8views\Plugin\views\filter;

    use Drupal\views\Plugin\views\display\DisplayPluginBase;
    use Drupal\views\Plugin\views\filter\InOperator;
    use Drupal\views\ViewExecutable;

    /**
     * Filters by given list of node title options.
     *
     * @ingroup views_filter_handlers
     *
     * @ViewsFilter("d8views_node_titles")
     */
    class NodeTitles extends InOperator {

      /**
       * {@inheritdoc}
       */
      public function init(ViewExecutable $view, DisplayPluginBase $display, array &amp;$options = NULL) {
        parent::init($view, $display, $options);
        $this-&gt;valueTitle = t('Allowed node titles');
        $this-&gt;definition['options callback'] = array($this, 'generateOptions');
      }

      /**
       * Override the query so that no filtering takes place if the user doesn't
       * select any options.
       */
      public function query() {
        if (!empty($this-&gt;value)) {
          parent::query();
        }
      }

      /**
       * Skip validation if no options have been chosen so we can use it as a
       * non-filter.
       */
      public function validate() {
        if (!empty($this-&gt;value)) {
          parent::validate();
        }
      }

      /**
       * Helper function that generates the options.
       * @return array
       */
      public function generateOptions() {
        // Array keys are used to compare with the table field values.
        return array(
          'my title' =&gt; 'my title',
          'another title' =&gt; 'another title',
        );
      }

    }


Inside the plugin, you need to override three methods, as explained in Creating a custom Views filter in Drupal 8. Here is a quote from it:


  Inside init(), we specify the title of the set of filter options and the callback that generates the values for options. This callback has to be a callable and in this case we opted for the generateOptions() method on this class. The latter just returns an array of options to be presented for the users, the keys of which being used in the query alteration. Alternatively, we could have also directly created the options inside the init() method by filling up the $this-&gt;valueOptions property with our available titles. Using a callback is cleaner though as you can perform various logic in there responsible for delivering the necessary node titles.
  
  The point of overriding the query() and validate() methods was to prevent a query and validation from happening in case the user created the filter without selecting any title. This way the filter has no effect on the results rather than returning 0 results. It's a simple preference meant to illustrate how you can override various functionality to tailor your plugins to fit your needs.