Neveralla (aka Osborne Prolific) is the only fig variety about which I've read that it might be somewhat shade tolerant. You might also consider keeping a fig in a pot if that allows you to put it in a sunnier spot. Pretty much any fruit tree requires ample sun to produce quality fruit.

How many hours of direct sun does the average fig require?

Brogiotto Nero
Read the passage attached from Pomona Italiana di Georgio Gallesio.
About a third of the way from the bottom of the description, it talks about how shade tolerant Brogiotto is.

Here is a link that might be useful: Brogiotto Nero

We've had a fig tree on our property for about 25+ years, and it's been growing in probably 75% shade since being planted. It's either celeste or brown turkey from what I'm told, although I didn't buy it and can't confirm what it is.

Almost every year, it produces many figs, enough for fresh eating, freezing, and enough for the birds and squirrels.

Keep in mind though....and Al or Dan please correct me if I'm wrong.....that those of us in zones 9 & 10 can probably get away with less direct sunlight on our trees than someone in a cooler climate with a shorter summer.

I will be shading some of my new figs this first season, as we have temps above 100 for extended periods of time, and temps above 110 are common June thru September.

I'm in z8 with a Brown Turkey on the north side of my 2.5 story house) in full shade - 80%-90% shade - and it fruits just fine.

The main deteriment I've found to this setup is that temps are different on that side of the house, so the sahde is forcing a shorter season. Bud break and dormancy happen much later than other trees in full sun. Fruit production is around 40%-50% less than trees I know in full sun, and I can't comment on quality, because I'm not a huge fan of the taste of BT. They taste the same as any other BT I've had. My wife likes them, if that helps?