Modern Vespa

Since I got this scooter the fuel gauge always shown less fuel in tank then it is.
After filling tank to max the gauge is not showing full.
If I fill tank when reserve lamp glows up I get 6-6,5 liters on it.

Is there some adjusting possible?

Not really. The tank holds ~9.2l, and the reserve is meant to be ~2l. Many if not most 300's of that era show the same low fuel as yours, sadly. My 2010 300 is the same.

If you really, really wanted to, you could drop the fuel tank and replace the sender - but I bet it'd not be any more accurate. I just allow at least another 30 miles (50km) before I insist on refuelling. However, it's often more convenient to refuel sooner - about to pass near your favourite filling place, or a good price perhaps.