To clarify what I said, shade does not affect the size of fruit (at least dramatically enough to notice).
Figs that are smaller sized varieties naturally (think Celeste/Chicago Hardy vs larger ones like Brunswick or Kadota) in my experience tend to ripen faster. That may be why some of the smaller varieties tend to be earlier varieties on their own as per Ottawan.
Sorry if it sounded like I said shade would give you smaller fruit. I meant if you have shade, go with smaller fruit since those tend to be less sun hungry. I could be wrong but I've only seen success in partial shade with small sized figs.
When growing things in shade I keep these generalizations/basics in mind:
1. A fruit that is smaller sized to start with (a raspberry vs. an orange) will likely need less photons of energy. Also a small bush vs. a large tree. The more mass there is and the more surface area there is, the more sun it may want to eat up for all its own molecules. This applies to figs in that fruit like Kadota if it's going to make a massive fruit it might take weeks from when its full size fruit to now when it changes color and ripens fully. As opposed to my Chicago hardy a smaller fruiting fig, once reached full size fig but green ripens fast in a couple days.
2. Any lay lowing fruiting plant is less sun crazy by heart as it is OK with being underneath the canopy (think dates... although small fruit--tall trees as heck.)
3. The tarter a fruit is (think a tart cherry vs. a fig) the less sun it needs. Anything without an end old goal of being super sweet won't be as affected by less sun. Sun sweetens fruit.
4. An earlier variety is best so even though it's shade and you're getting say 50% of the light you want, well it will certainly slow down the ripening but maybe you have enough time before frost since it's early variety to make up for total sun exposure. Example, I have a chicago hardy in a couple hours of shade, it just ripens a week later than it should which it can afford to and still ripen with plenty of time before frost.
5. Production and flavor will be affected. Ripening at half speed, is not same as ripening at full speed. In terms of productivity--with citrus, not enough sun can limit blossoms from the get go.
6. Can the fruit ripen well off tree indoors picked? If so may be ok with less sun. I.e. persimmons.
Anyway, these are just basic common sense and also just generalizations with many exceptions. But keeping these in mind you can deduce most case by case shade questions across most fruits.
If you got shade, go with raspberries, blackberries, blueberries, and pawpaws!