Hi Sandesh,
Let's start with the Webex Contact Center GUI. The Recording Management module will appear if the Agent is allowed access to the recordings. This is according to the Configure Webex Contact Center Call Recording Settings document. I see no mention of an API in that document.
I looked in the Cisco Webex Contact Center Desktop Developer Guide but the only references to 'recording' I found were in regards to pausing and resuming recording.
According to What's New in Cisco Webex Contact Center:
"08 March 2021
Download Call Recordings
Administrators and Supervisors can download recordings of calls that were handled by Agents. A new API will be available to enable downloading of the recordings."
Please notice there is also a 'Coming Soon' tab, as well as a button to 'Subscribe To This Article'.
According to Cisco Webex for Developers - API Reference - Recordings, a user can only List, Get Details for or Delete a Recording.
In short, I haven't found a way to download the recordings yet, but it looks like somethings which may be available soon.