I also have a huge outdoor balcony with little sun, Zone 6, maybe 7ish. The corner gets 2-4 hours direct sun. Gathered from this post
https://permies.com/t/10302/Shade-Tolerant-Edibles
What trees will produce indoors or in a shaded balcony?
Annual Lettuces
Endive
Chard
Mints
Sorrel
Ginger
Fiddleheads of Pako Ferns, High Climbing Ferns, Swamp Ferns
Spinach
Beets
Akebia a.k.a. Chocolate Vine (fruit)
Scallions
Pawpaw
Blueberries
Actinidia (fruit)
Violas
Mushrooms
Strawberries?
asparagus
cucumber
blackberries
raspberries
basillycum
American Persimmon
Bunya Bunya
Ginkgo
Service Tree
Blackhaw
California Hazelnut
Blue Banana Bean
Chokeberry
Currant
Elaeagnus X ebbingei
Evergreen Huckleberry
Gooseberry
Goumi
Honeyberry
Oregon Grape
Red Huckleberry
Salal
Salmonberry
Serviceberry
Arctic Beauty Kiwi
Himalayan Damarru
Japanese Wineberry
Magnolia Vine
Sausage Vine
Stauntonia
Bear's Breech
Comfrey (for fertilizer)
Japanese Coltsfoot
Miner's Lettuce
Nettles
Ramps
Violet
Waterleaf
California Bay Laurel
Garlic Mustard
Sweet Woodruff
Wild Ginger
Alpine Strawbeny
Bunchberry
Emerald Creeper
Himalayan Bramble
Chinese privet
Devil's club
English laurel
Black raspberry
Ginsing
Mitsuba
Siberian or Pink purslane
Sweet cicely
Tarragon
Watercress
Linden
Blackberry
Plum yew
Flowering quince
Goji berry
dwarf chestnut
Beech
Mountain pepper
Blue or black elder
New Zealand
flax
Creeping dogwood
Wintergreen
Nepalese raspberry (very shade tolerant)
Creeping bramble
Chinese bramble
Ground elder
Wild garlic
Wild angelica
Columbine
King's spear
Lady's smock
Good King Henry
Golden Saxifrage
Mock strawberry
Sweet woodruff
Aleroot
Hosta (yes, young leaves are edible)
Mallows
Lemon balm
Plantain
Solomon's seal
False Solomon's seal
Lesser switchwort
Violet
Sweet coltsfoot
Primrose
Rhubarb
Garlic mustard
Hog peanut
burdock
land cress
calendula
rampion
Hedge mustard
Black lovage
Groundnut
Sweet tea vine
caucasian spinach
Old Man's beard
wasabi
sprouts
mushrooms
mint
partial shade-tolerant vegetables
Arugala
Rutabagas
Beets
Salad Burnet
Broccoli (Can't testify for this one, but I'd say it wouldn't get very big)
Salsify
Brussels sprouts (Mine did poorly)
cabbage (Mine did poorly)
Cauliflower (Can't testify for this one, but I'd say it wouldn't get very big)
Summer Squash
Celery
Turnips
Angelica
Kale
Borage
Kohlrabi
Caraway
Leeks
Coriander
Parsnips
Potatoes (Didn't do well for me in the shade)
Tarrgon
Pumpkins (Didn't do well for me in the shade, unless you like small pumpkins)
Thyme
Radish
Other noteworthy ones:
mustard greens
pak choi
cardamom
peas
bush beans
currants
gooseberry
Commelina cyanea aka scurvy weed
Tetragonia tetragonoides Aka New Zealand spinach