Is there any method to extract transactions for an bitcoin address which is not in my wallet using bitcoin core? I have setup Bitcoin core and trying build an API to fetch all transactions under an address ( not in my wallet ).

Bitcoin core RPC documention says that an address which is not in my wallet needs to be imported. So I did the same using importaddress while setting rescan true e.g. importaddress '35z3Re9SgLHBfeg7y1HdR35t9HrTqTsKFV' 'test' true. It took more than a week to rescan the whole blockchain database. 

After importing the address, when I issued the getaddressinfo RPC command I got empty set of transactions in response.

Am I missing something ? Can you please help me here with the steps ?
You can use the scantxoutset command to scan for unspent outputs for a given address (or script). 

Importing an address adds it to your wallet, and you will see transactions for imported addresses under the listreceivedbyaddress and listtransactions commands.