Do I need internet connection to use generative fill on photoshop?

Some tools give you an option of using the cloud or keeping it local which can be set in Prefences.

However, Generative Fill, and Firefly, both operate on Adobe's servers as the Ai uses a vast store of stock images to build and add to your image, so there is no choice.  You have to be online to use them.

Plus Photoshop needs you to log in once a month or so to authorise your subscription

Yes you need an internet connection to use Generative Fill.