How to check category has Sub category on 1 level and 2 level in magento?

SO you have the main category id...

$categoryId = 9;

//get the category object

$category =
Mage::getModel('catalog/category')

  
->setStoreId(Mage::app()->getStore()->getId())

  ->load($categoryId);

Remember that all categories have a path setting where all the category tree from root to the category in question is kept. Something like: 1/2/5/27.
Now all you need to do is check if there is a category with the path that starts with the path of your main category and is 2 levels down.

$collection =
Mage::getModel('catalog/category')->getCollection()

   
->addPathsFilter($category->getPath().'/')
//this will add a filter 'where path like '$path%''

   
->addAttributeToFilter('is_active',
1)//if you want to check if there are enabled grandchildren

   ->addAttributeToFilter('level',
$category->getLevel() + 2);// search for categories 2 levels down.

Now all you have to do is see if there are items in your collection.

if ($collection->getSize()
> 0) {

    //$category
has grand children

}

else{

    //$category
does not have grand children

}