if ($ajax_handler->is_success) { // only if no errors in previous verification/actions
global $wpdb;
$form_id = $_POST['form_id']; // only for current form
$email = $fields['email']; // change email field Custom ID if different
$sql = 'SELECT count(*) FROM '.$wpdb->prefix.'e_submissions AS es, '.$wpdb->prefix.'e_submissions_values AS esv WHERE es.id = esv.submission_id AND es.element_id = "'.$form_id.'" AND esv.key = "email" AND esv.value = "'.$email.'"';
$count = intval(reset($wpdb->get_col( $sql )));
if ($count > 1) { // you can set an higher limit, now single submission
wp_send_json_error([
'message' => 'Once per email!', // customize error text
'data' => $ajax_handler->data,
]);
}
}