Not ideal as I'm sure you are aware. I'd stick with leaf and root veggies, such as lettuce, carrots, radishes, beets, and similar. You probably won't get much results at all in winter, so I'd plant for spring thru fall harvests.

You could try a "cherry" type tomato like 'Sweet 100', but don't expect a lot of yield, or sweetness.

I want to bump this post up because I've an identical situation on a side yard, with maybe an extra hour or so in the summer of morning sun. I would like to hear more suggestions.

I want to bump this post up because I've an identical situation on a side yard, with maybe an extra hour or so in the summer of morning sun. I would like to hear more suggestions.

Vegetables are sun loving plants, so your options are limited. A package of vegetable seeds can be had for 99 cents, so try what you want to try and see what happens. Perhaps something that climbs up vertically, like peas, could get a little more sun that way.

I grow Swiss chard, carrot,and kale like that; they actually have been in part shade for over a year.

I have to water less.

Was able to get indigo rose tomato, peas, okra, beans and a sugar baby watermelon for summer.

I'm all containers on a rooftop

The watermelon vine grew to the sun but set fruit in the shade, hope that helps.