Hello Rangab,
There are no any default api according to your requirement. You have to create your own rest/soap API.
Check out here how to extend rest api in magento.
code for getting associate products for a configurable product
$product= Mage::getModel('catalog/product')->load($configId);
#Check if the product has children
if ($product->type_id == 'configurable') {
$options = array();
// Get any super_attribute settings we need
$productAttributesOptions = $product->getTypeInstance(true)->getConfigurableOptions($product);
foreach ($productAttributesOptions as $productAttributeOption) {
$options[$product->getId()] = array();
foreach ($productAttributeOption as $optionValues) {
$val = $this->trimValue($optionValues['option_title']);
$options[$product->getId()][] = array (
$optionValues['sku'] => $optionValues['attribute_code']."=".$val
) ;
}
}