How to display data using block code?

You not need to create any controller but you have to create block class.

So,you have to create a module should have this command files:

app/code/{Vendor}/{Module}/composer.json app/code/{Vendor}/{Module}/registration.php app/code/{Vendor}/{Module}/etc/module.xml 

then create a block file app/code/{Vendor}/{Module}/Block/BlockName and write a function and return children category from this function to phtml.

Block Class

<?php namespace {Vendor}\{Module}\Block use Magento\Framework\View\Element\Template; class BlockName extends \Magento\Framework\View\Element\Template implements \Magento\Framework\DataObject\IdentityInterface { /** * @var \Magento\Catalog\Model\CategoryFactory */ private $categoryFactory; public function __construct( \Magento\Catalog\Model\CategoryFactory $categoryFactory, Template\Context $context, array $data = []) { parent::__construct($context, $data); $this->categoryFactory = $categoryFactory; } const CATEGORYID = 65; public function getSubCatgories() { $category = $this->categoryFactory->create(); $category->load(self::CATEGORYID); return $category; } /** * Return unique ID(s) for each object in system * * @return string[] */ public function getIdentities() { return [\Magento\Catalog\Model\Category::CACHE_TAG, \Magento\Store\Model\Group::CACHE_TAG]; } } 

and phtml Code is

<div> <h3> <a href=""> <?php $category =$this->getSubCatgories(); if(category){ $childrenCategories = $category->getChildrenCategories(); echo $category->getName(); ?> </a> </h3> <ul> <?php foreach($childrenCategories as $childrenCategory) { echo "<li>" . "<a href=" . $childrenCategory->getUrl() . ">" . $childrenCategory->getName() . "</a>" . "</li>";} ?> </ul> <?php }?> </div>