Mohan,
I dont think thats how it works.
Here's my understanding.
The SessionId in the Selenium world is not the same as the SessionId as used in a typical web application context.
Selenium basically uses the SessionId to associate/identify as to which server process should the client be talking to. The client could either be your tests or it could be a Selenium node, which receives a new session request from the Hub.
If you would like to spin off a new browser (powered by webdriver) which wants to re-use an existing application session (Not the webdriver session), then all you need to do is to export the set of cookies from your first session, persist it in memory, and then once your new browser comes up via webdriver instantiation, you inject those cookies into the new instance.
You might have to open up the corresponding web page, prior to doing this. I am not sure on that part, because I have never done it.
But driver.getSessionId() has got no role to play in this entire exercise.
In terms of the error you are facing, you would need to add some details pertaining to what version were you working with for Selenium/IEDriverServer/EdgeDriver/Browser version etc., and also furnish a sample test that could be executed to reproduce the problem that you are seeing!