No, there isn't one, but I'd like one. There's a cadre of turkey hunters, including me, who prefer the 20 over the 12 because of a combination of lightness and lethality. With the development of new metals for shot with densities greater than lead, the 20 gauge has the lethality of a 12 gauge of 10-15 years ago.

I have owned the Ithaca NID 10 in 3.5" and the Mag 10 Ithaca auto. I abandoned them for the Mossy 835 for turkeys because of weight. I went from the 835 to the SBE. Both of the 12s now stay in the safe; for the past 3 seasons, I have carried a Youth Model Mossy Super Bantam in 20 gauge. It is tailor made for turkeys shooting my handloads of 1 5/8 oz. of tungsten 9s. Puny 9s? Not exactly. There are 340+ tungsten 9s in an ounce. There are 585 lead 9s in an ounce. The patterns are incredibly tight and the best choke is about .570. The penetration of tungsten is superior to lead because of small profile, density and hardness. It doesn't deform. Shooting tungsten in 12s is overkill. It is incredibly expensive, but shell cost is the cheapest part of turkey hunting. My Mossy 20 weighs 5.25 lbs. out of the box. The Trijicon Reflex amber dot sight, 4 ozs. With sling, PG choke, slip on pad to increase LOP and foam comb with neoprene sleeve, the weight is probably 6 lbs. It's quite a turkey killer, but it is no Ithaca. The trigger is miserable and not much can be done about it.

I would love a M37 in 3'' 20 gauge with camo synthetic stock and forearm, sling mounts and a plain barrel with deerslayer type sights BUT with tritium in the leaf and post for early morning and old eyeballs. No bluing on metal, please. Coatings are superior for wear and corrosion resistance. Firesights or fibre optics are not enough for my eyeballs under a thick canopy with an early flydown.
Drilled and tapped for optics would be nice. I would like to substitute an M37 for this Super Bantam 20
(the contraption below it is a 100+ year old roll crimper that I use to handload):

Not in 20 gauge.
Gil

Ya that's interesting...wonder why they don't make it in 20? I own a featherlight 12g but my family has a 20 and 16g shotguns (nonithaca).

There's probably just not that much demand for it, although the 12 gauge TS is not that much more than an 870 factory tricked-out for turkeys. I'd love to have one in 20. I'm wondering if it would be possible to special order the 20 gauge defense gun with a 20-22" barrel....

I have a Model 37 - 20 gauge with a 26 inch ported barrel with a extra full turkey choke tube.
This barrel has fibre optic rifle sights and was constructed in Kings Ferry, New York.
The barrel itself is ported just before the front sight on both sides at 10 and 2 o'clock.
It is not camo nor synthetic but I would like to get a camo synthetic stock and forearm.