Autocomplete function for textfield of Form API

First, Create autocomplete controller and the route

Example of the controller : DefaultController.php

<?php

namespace Drupal\mymodule\Controller;

use Symfony\Component\HttpFoundation\JsonResponse;

use Symfony\Component\HttpFoundation\Request;

use Drupal\Core\Controller\ControllerBase;

class DefaultController extends ControllerBase{

  /**

   * Returns response for the autocompletion.

   */

  public function autocomplete(Request $request) {

    $matches = ['Value 1', 'Value 2', '... ...'];

    return new JsonResponse($matches);

  }

}

Example of the route : mymodule.routing.yml

mymodule.autocomplete:

  path: '/mymodule/autocomplete'

  defaults:

    _controller: '\Drupal\mymodule\Controller\DefaultController::autocomplete'

  requirements:

    _access: 'TRUE'

Then add this route to the field

Example :

$form['myfield'] = [

  '#type' => 'textfield',

  '#title' => t('Autocomplete text field'),

  '#autocomplete_route_name' => 'mymodule.autocomplete',

];

See Entity Autocomplete From here