Fruit in Shade

Help!
I have an easterly facing apartment balcony; it is overshadowed by a
balcony above, and there are trees on the far side of the street,
adding to the sunblock effect. That said, it does get a lot of morning
sun****ne and in summer a lot of heat. I would love to grown fruit on
it. Does anyone know of any fruit that might have a shot at survival?

Thank you.