Can I use Sora FD-3503 on MTB crankset 44-32-22?
The tech document says the max chainring difference of sora is 20t and min difference top and intermediate is 11T.

I'm not going to look up the spe, but will tell you what to consider.

1st, the overall range of your crankset is 2 teeth greater than the stated capacity. There's usually some fudge room, so it's still possible that you can get it low enough for the chain to clear the bottom back of the cage when on the 22t. However it's super close.

2nd, unless the sora is made for compact drive cranks, the curve of the cage won't match the chainrings properly. That puts the cage farther back then ideal, especially on the smaller rings. This worsens shift response, and can crate trim problems when the chain comes from angles.

That's the info, now you have to make your own assessment.

Shimano's ft ders have very specifically shaped cages which help guide, lift or clear the chain. These tend to be best matched with the chainring teeth counts especially if you're using an indexed lever. But the proof is in the pudding and I've seen some non spec combos work well enough for their owners to be happy. At one time I thought there was a difference between Shimano's road and MtB cranks WRT the rings' c-c distancing. There most certainly is a difference between road and MtB shifters and their respective ft ders WRT cable pull ratios. This is why some touring bikes use bar end levers (with the friction ft) when using MtB ders and cranks. Andy.

I'll give an apple to bananas comparison using an Altus FDER.
I swapped my 28-38-48 to a 22-32-44.
It worked OK, but shifts were probably a bit less "pristine".
You "might" find that playing with the gap between the large ring & cage "might" make a difference.

I'll provide a different perspective. Yes, it will work and shifting won't suffer. I've been using a Tiagra road derailer since around 2004 shifting a 46/36/20 crank on my touring bike. I'm also using STI shifter which is more demanding than bar end shifter in the setup. I've never had a shifting problem. Front shifts, up and down, are crisp and clean.

Matching the curve of the derailer to the curve of the chainring is a red herring, in my opinion. I've used the same model of derailer to shift 52 tooth, 50 tooth, 48 tooth and 46 tooth chainrings. There is no performance difference between any of them.

As long as the curve has a large enough radius to clear the big chainring I pretty much agree. In the late '90's Trek used an RX100 front derailleur (designed for a 52T big ring) on their 1220 with an RSX 46/36/26 triple crank and it shifted just fine with RSX STI brifters.

The exception would be using an MTB front derailleur with the cage curvature designed for a 42T or 44T big chainring on a 52 or 53T road crank. The fd would have to be positioned so high that shifting would certainly suffer.

you can try, and then learn 1st hand.

Note the difference the diameter makes between 53 t and 44t.

say you use 53 x .5 : is 26,5" around, 44 x.5 = 22"

so what is the diameters?

https://math.about.com/library/blcirclecalculator.htm

the arc of a Road FD is made to be closely following the larger diameter

a compact MTB to match the smaller arc ..

When I used a road front derailleur on a mountain crank, I discovered that it helped if I raised the derailleur higher than I would normally. Instead of a 1mm clearance for the cage to tooth, I did 5 or more mm distance. Allowed the inner cage to work better with the middle chainring.