possibly carrots.

I think Grapes prefer a non fertile soil?

Both carrots and grapes grow well on poor soil though for the carrots it needs to be a very fine tilth (soil) with no stones. In the wine growing regions grapes grow on soil that is little more than limestone with tiny pockets of soil - hence the long tap root to get to the water table. Just about everything else requires a good well manured/composted soil.

It's a bit of an ambiguous question. With very few exceptions I think just about every vegetable plant would prefer a fertile soil.

If you mean which vegetables would tolerate a poor soil more then I'm sure that there are many. Clay is considered as a poor soil for plants because of poor drainage and the ability to hold nutrients, etc, so I think that most of the root crop vegetable might be worth looking at?

have you thought about herbs,

My mum has clay soil but she manages to grown runner beans, cabbages, and onions fine

Clay soil has a lot of nutrients locked in it - just needs good organic matter and possibly fine grit to open it up a little. Potatoes will do fine on clay as will brassicas and legumes. Tap rooted vegetables will struggle.

Carrots it is then. Thanks

Make sure in that case that you have avery fine tilt with no stones and protect from root fly - oh and good luck!