Hello @anithabanothu,

Good day!!

To enhance the performance of your helpdesk, Freshdesk will archive closed, inactive tickets. Depending on your ticket traffic, any 'closed' ticket that has been inactive for 120 days will be archived. You can read about ticket archiving here: 

https://support.freshdesk.com/en/support/solutions/articles/212901-ticket-archiving

I’m afraid that we wouldn’t be able to archive the tickets by using API. However, you will be able to View the Archive tickets, delete the Archive Tickets, and view all the conversations on the Archive ticket.
Here is documentation that might help:

https://developers.freshdesk.com/api/#archive_tickets

Feel free to drop in a note here for any further questions:)