I have gone throught the AMP start guide, but they have not mentioned anything about Jekyll.
Is there any kind of special modification, we need to do for the jekyll website to use AMP in it?
There are several AMP themes, which you might be able to use or adapt:
Yes. You need to include the AMP scripts in your layout. And do some markup changes for things like AMP images.
There are several Jekyll AMP themes out there to give you an idea of what needs to be done. There is also a Jekyll plugin which does some of the AMP markup generation for you.