Most tomatoes will grow quite well in mostly shade. But they tend to produce overly large foliage to capture as much light for photosynthesis as possible. And even with a more shade tolerant or short/early harvest cultivar, less than 4 hours of direct sun a day will seriously limit flowering and fruiting and they will not be very productive.

Cherry tomatoes do well with less direct sun compared to the big boys. Sungold cherry is our favorite.

I'll add to these good comments and echo that with less sun, you just expect less fruit. The plants will grow fine. So there are gradations of "successful".

I'd look for a variety bred for containers, and yes, small fruited types tend to be somewhat easier to grow, IMPE.

Choose variety suitable for your location,not hours of sun. You can add sunlight through reflection. A white wall,sheet or object in right position will increase usable light. Be cautious with mirrors or foil so that you don't over-do-it. That is to say when sun is fully on plants don't place mirror or foil to focus full sun on plants from a secound direction. I have successfully started seedlings in North windows by placing a U of foil around them.

A white wall or sheet, and even foil, will only provide much light if sunlight is hitting that whiteness directly. Might as well put your tomatoes there. I have white walls in a north-facing room, and no way can I grow plants properly in that room. You can start seedlings with hardly any light at all. The issue is how much they get as they mature.

Dan I don't have time nor inclination to explain this so you understand so feel free to not even trying to understand.