Shady Vegetable Garden

The following crops will produce with three to six hours of sun, or fairly constant dappled shade, per day.

Salad Greens, such as leaf lettuce, arugula, endive, and cress.
Broccoli
Cauliflower
Peas
Beets
Brussels Sprouts
Radishes
Swiss Chard
Leafy Greens, such as collards, mustard greens, spinach, and kale
Beans

Fall planting, the advice for Houston at this time (Sept.) is to plant:
Beans
Parsnips
Turnips
Potatoes
Carrots
Broccoli
Cauliflower
Winter Squash
Might also try for cucumbers which really should be August.