Hook_views_field_data_alter(). implement this hook if you want to modify the handler for any field provided by field api. Otherwise use Hook_views_data_() if you want to expose new table to view.

hook_views_data_alter.php

<?php
 /**
 * Implements hook_field_views_data_alter().
 */
function MYMODULE_field_views_data_alter(&$result, $field, $module) {
  if ($field['field_name'] == 'FIELD_NAME') {
    $name = $field['field_name'];
    foreach ($result as $table_name => $table_data) {
      if (isset($table_data[$field['field_name']]['field'])) {
 // HERE modifying filter handler. But we can modify sort, field, contextual filter and argument handler in same way
        $result[$table_name][$field['field_name'] . '_value']['filter']['handler'] = 'FILTER_HANDLER_NAME_IN_SEPARATE_FIEL';
      }
    }
  }
}