Most fruits want full sun to set and ripen the fruits or berries. You could try something like rhubarb or some type of more woodland species like huckleberries (Vaccinium ovatum or parvifolium) but you won't have much luck with things like blueberries, raspberries, strawberries or grapes - they need at least 6 hours, would prefer more.

Gooseberries grow well in partial shade and are hardy plants. They are tart but as they ripen develp a sweeter taste. They have thorns and the berries are unusual and beautiful to look at. T

I concur with the above, and have had good luck with black currants in partial sun. Good luck.