Here is the honest version, because most advice on this dodges it: you cannot grow fruit in the shade. Tomatoes, cucumbers and anything that has to ripen need sun, and no amount of feeding substitutes for it. If your garden gets less than four hours of direct sun, those crops will grow and then disappoint you.
What a shaded garden grows very well is leaves. Lettuce Mix, Lettuce Romaine, Giant Spinach and Chard Green Broad all prefer partial shade, and in a hot summer they do better there than in full sun, because shade is what stops them bolting. A north-facing bed is a salad bed, and a good one.
Turnip Purple Top tolerates it. Red Beet will give you smaller roots but perfectly good leaves. The brassicas and the carrots want the sunniest spot you have.
So the rule is simple: put the leaves in the shade, the roots in what sun you have, and grow the fruiting crops in a pot you can move to the brightest corner.
