I am new magento... I want to know do we have any paid or free extention to connect ICICI Easypay payment gateway integration with magento and to make it one of the payment method in magento
Yoy have a few options on MagentoConnect: https://www.magentocommerce.com/magento-connect/catalogsearch/result/?q=icici&pl=0
You should check which option fits better for you.
I guess you should check here https://marketplace.magento.com/catalogsearch/result/?q=icici
Yes, a few paid extensions available that help you connect ICICI Easypay payment gateway integration with Magento. They are: