Add following code 

    $catId = 3; // Parent Category ID
    $objectManager = \Magento\Framework\App\ObjectManager::getInstance();
    $subcategory = $objectManager->create('Magento\Catalog\Model\Category')->load($catId);
    $cnt = 0;
    $subcats = $subcategory->getChildrenCategories();
        foreach ($subcats as $subcat) {
            $cnt++;
            echo $subcat->getName();
            if($cnt == 4)
                 break;
        }
    }