About 10 years ago, I lived in a house with a backyard so shady, it barely got any sunlight at all. Since summers are very hot down South, it was really nice because I could sit outside or play with my dog without getting a sunburn (like I do in my current yard). The downside is there weren’t any places for me to grow a garden.
Eventually, I chose a spot on the side of the house that got more sunlight, but even then I had to dig up a large bush and prune some tree branches. The spot still only got a few hours of sunlight a day, but that was just enough for the vegetables I planted.
Maybe you have a similar problem with your backyard. Fortunately, if you can find a way to get 3 or 4 hours of sunlight in one area, you can plant a wide variety of herbs and vegetables that only need a few hours of sunlight a day.
This article by Attainable Sustainable lists several options.