Not many vegetables grow well in shade
I am not aware of many vegetables that grow well in the shade.
Ginger can, though even ginger prefers filtered sunlight.
I read this on a site (VEGETABLES FOR THE SHADY GARDEN) after seeing your question :
"In general, leafy vegetables are the most shade-tolerant, while those that fruit from a flower (tomatoes, peppers, squash, eggplants) are the least. In between are the root vegetables requiring at least a half day of full sun: potatoes, beets, carrots and turnips. Shade tolerant leafy vegetables include lettuce, spinach, Swiss chard, arugula, endive and radiccio. Broccoli (and its relatives -- kale, kohlrabi, turnips, mustard and cabbage -- also grow in partial shade.
Leafy vegetables display another advantage: they can be picked and enjoyed at any stage of maturity, unlike sun-loving vegetables that must ripen."
Try google, you will find more answers.
Regarding growing in a balcony : keep the potted soil well aerated ... mix some sand in it. The usual mistake is to use clayey soil and then over-water it (because the more you love the plant, the more you tend to water it

)