Forgot to mention, I am in the SF bay area, in San Carlos specifically (San Mateo county, peninsula).

Very narrow area, that will be difficult. Maybe think up, not out: what about vines like Kiwi, pole beans in summer and peas in winter?

Citrus wants full sun.

There are vining hydrangeas.

Blueberries do okay in morning sun/afternoon shade, but give them the 3' wide spots, not the 1.5' wide spots. You get fruit but it isn't as sweet as it is with more sun. Also net or cage the plants so birds/rodents don't get all the fruit.

Bell Peppers do better with some shade and they are small plants that would fit.

Sonali, considering the setbacks on typical properties in SF Bay Area, I am wondering if your side yard may be actually about 5ft wide, with 1.5-2ft of planting area and the rest paving?

If such is the case, then you can easily plant semi-dwarf varieties of fruit trees like Peach or Apricot (my neighbor has it exactly in similar spot and they are going gangbusters). With semi dwarf sizes, the tree crown can go over the fence and get plenty sunlight.

Blueberries would do well as well but you will have to carefully maintain acidity in the ground. If you decide to mix edible and ornamentals, consider Azaleas and Camellias distributed with Blueberries.

Another suggestion is birch fern (or fern birch?) -- It's a very vertical growing ornamental plant with leaves looking like fern. It will provide a good privacy screen if such is your intent.

Lastly, if your aim is to purely provide a green touch, try a passion vine or jasmines. They will fill the wall in no time.