<?php
require_once('app/Mage.php');
Mage::app();

$yourCategory = Mage::getModel('ultimate_mars/category');
if(isset($_REQUEST["attributeCode"])){
    $categryCode = $_REQUEST["attributeCode"]; /*  category code */
    $yourCategory = $yourCategory->load($categryCode,"producttype");
}
else{
    $yourCategory = $yourCategory->getCollection()->addFieldToFilter("parent_id",1)->getFirstItem();
}
/* Getting subcategory of requested category code */
$cat_model = Mage::getModel('ultimate_mars/category');
$_categories = $cat_model->getTreeModel()->getCollection()->addFieldToFilter("parent_id",$yourCategory->getId());

$category = array();
foreach($_categories as $_category)
{
    $category[] = array("name" => $_category->getCategoryname(), "id" => $_category->getEntityId());
}

echo json_encode($category);

<?php

    class Ultimate_Mars_Model_Category extends Mage_Core_Model_Abstract
    {

        const ENTITY    = 'ultimate_mars_category';
        const CACHE_TAG = 'ultimate_mars_category';

        protected $_eventPrefix = 'ultimate_mars_category';

        protected $_eventObject = 'category';

        public function _construct()
        {
            parent::_construct();
            $this->_init('ultimate_mars/category');
        }

        public function getSelectedProductsCollection()
        {
            if (!$this->hasData('_product_collection')) {
                if (!$this->getId()) {
                    return new Varien_Data_Collection();
                } else {
                    $collection = Mage::getResourceModel('ultimate_mars/product_collection')
                            ->addFieldToFilter('category_id', $this->getId());
                    $this->setData('_product_collection', $collection);
                }
            }
            return $this->getData('_product_collection');
        }

        public function getTreeModel()
        {
            return Mage::getResourceModel('ultimate_mars/category_tree');
        }

        public function getTreeModelInstance()
        {
            if (is_null($this->_treeModel)) {
                $this->_treeModel = Mage::getResourceSingleton('ultimate_mars/category_tree');
            }
            return $this->_treeModel;
        }

        public function getParentCategory()
        {
            if (!$this->hasData('parent_category')) {
                $this->setData(
                    'parent_category',
                    Mage::getModel('ultimate_mars/category')->load($this->getParentId())
                );
            }
            return $this->_getData('parent_category');
        }

        public function getParentId()
        {
            $parentIds = $this->getParentIds();
            return intval(array_pop($parentIds));
        }


        public function getParentIds()
        {
            return array_diff($this->getPathIds(), array($this->getId()));
        }


        public function getAllChildren($asArray = false)
        {
            $children = $this->getResource()->getAllChildren($this);
            if ($asArray) {
                return $children;
            } else {
                return implode(',', $children);
            }
        }

        public function getChildCategorys()
        {
            return implode(',', $this->getResource()->getChildren($this, false));
        }


        public function checkId($id)
        {
            return $this->_getResource()->checkId($id);
        }


        public function getPathIds()
        {
            $ids = $this->getData('path_ids');
            if (is_null($ids)) {
                $ids = explode('/', $this->getPath());
                $this->setData('path_ids', $ids);
            }
            return $ids;
        }

        public function getLevel()
        {
            if (!$this->hasLevel()) {
                return count(explode('/', $this->getPath())) - 1;
            }
            return $this->getData('level');
        }


        public function verifyIds(array $ids)
        {
            return $this->getResource()->verifyIds($ids);
        }

        public function hasChildren()
        {
            return $this->_getResource()->getChildrenAmount($this) > 0;
        }

        public function getCategorys($parent, $recursionLevel = 0, $sorted=false, $asCollection=false, $toLoad=true)
        {
            return $this->getResource()->getCategorys($parent, $recursionLevel, $sorted, $asCollection, $toLoad);
        }


        public function getParentCategorys()
        {
            return $this->getResource()->getParentCategorys($this);
        }


        public function getChildrenCategorys()
        {
            return $this->getResource()->getChildrenCategorys($this);
        }


        public function getStatusPath()
        {
            $parents = $this->getParentCategorys();
            $rootId = Mage::helper('ultimate_mars/category')->getRootCategoryId();
            foreach ($parents as $parent) {
                if ($parent->getId() == $rootId) {
                    continue;
                }
                if (!$parent->getStatus()) {
                    return false;
                }
            }
            return $this->getStatus();
        }
    }

<?php
require_once('app/Mage.php');
Mage::app();

$yourCategory = Mage::getModel('ultimate_mars/category');
if(isset($_REQUEST["attributeCode"])){
    $categryCode = $_REQUEST["attributeCode"]; /* Your requested category code */
    $yourCategory = $yourCategory->load($categryCode,"producttype");
}
else{
    $yourCategory = $yourCategory->getCollection()->addFieldToFilter("parent_id",1)->getFirstItem();
}
$childLevel = (int)$yourCategory->getData("categorylevel") + 1;
/* Getting subcategory of requested category code */
$cat_model = Mage::getModel('ultimate_mars/category');
$_categories = $cat_model->getTreeModel()->getCollection()->addFieldToFilter("parent_id",$yourCategory->getId());

$category = array();
if($_categories->count() > 0){
    foreach($_categories as $_category)
    {
        $category[] = array("name" => $_category->getCategoryname(), "id" => $_category->getEntityId());
    }
}
else{
    $products = $yourCategory->getSelectedProductsCollection();

    if($products->count() > 0){
        foreach ($products as $product) {
            $category["products"][] = array("name" => $product->getProducttitle(), "id" => $product->getEntityId());
        }
    }
}
echo json_encode($category);