I want to get the unsubscription email flag through API only.
Is there any API present by which we can fetch the lead id along with what type of email he has unsubscribed?
"type of email" doesn't have any self-evident meaning in this context. (You really need to get a handle on how Marketo works before attempting to build integrations, or your questions will not make sense to users of the platform.)
If you run Describe Activities, you'll see Unsubscribe Email. This activity is logged whenever a lead's unsubscribe can be attributed to a specific email, including when they click the {{system.unsubscribeLink}} and when they click "Unsubscribe" button in an email client that supports the X-List-Unsubscribe header.