How can I check category have any child category with specific name ?
$category = Mage::getModel('catalog/category')->load($name, 'name');
but I want sub category from specific parent category.
you can try using category collection
$collection->addAttributeToSelect('*')
->addAttributeToFilter('parent_id',$parent_id)
->addAttributeToFilter('name', array(
'like' => '%amit%'
));
You can try This Code.
$category_model = Mage::getModel('catalog/category');
$_category = $category_model->load(13);
$all_child_categories = $category_model->getResource()->getAllChildren($_category);
print_r($all_child_categories);
here 149 is Category id you can replace with your own
$category = Mage::getModel('catalog/category');
$category->load(149);
$childrenString = $category->getChildren();
$children = explode(',',$childrenString);