A simple example Drupal Controller with a cached JSON Response.

CachingController.php

<?php

namespace Drupal\example\Controller;

use Symfony\Component\HttpFoundation\Request;
use Drupal\Core\Controller\ControllerBase;
use Drupal\Core\Cache\CacheableJsonResponse;
use Drupal\Core\Cache\CacheableMetadata;

class ExampleController extends ControllerBase {
  public function getJson(Request $request) {
    $data = [];
    // Do some useful stuff to build an array of data.     
    
    // Add Cache settings for Max-age and URL context.
    // You can use any of Drupal's contexts, tags, and time.
    $data['#cache'] = [
      'max-age' => 600, 
      'contexts' => [
        'url',
      ],
    ];

    $response = new CacheableJsonResponse($data);
    $response->addCacheableDependency(CacheableMetadata::createFromRenderArray($data));
    return $response;
  }
}