There have been variations on farming in swamps, and if you study the chinampa style of farming in central/south america you will find examples of swamps/wetland/lakes that have been modified to create raised beds with channels between.
These allowed for farming of various produce and have also been used to providing grazing for livestock. Furthermore, aquaculture is practiced in the channels of water between the fields.
Plants. Animals. Fish/Shellfish.
There are other/better links out there too if you keep digging.
Basically, you dredge the bottom of the swamp and start to stack the soil in an area. This builds the soil and raises it above water level as you continue to stack it.
This is stacked in an area where a "basket" has been prepared by using stakes and reeds woven together.
This basket forms the boundary of the "field".
I have also read that trees, such as willows, have been planted along the field edge. The willows roots grow to create a natural basket that is alive, versus dead wood that eventually rots away. You can see in various images from the links that there are these trees lining the boundaries of the fields.
These raised beds are made from stacking the dredged nutrient rich soil, and as they sit above water level, act sort of like a low-tech/passive organic hydroponics system by drawing water naturally from below.
Some additional benefits are that with the proximity to water, the temperature extremes of the climate are regulated owing to the function of water and it's ability to carry/hold heat.
Also, with the channels formed between the beds, aquaculture production of various fish/shellfish can be pursued.
Furthermore, the beds can be used for livestock.
All in all, an impressive adaptation.
In the amazon there was also a form of soil improvement/adaptation that was part of a process to continually improve fertility/arability.
I read about this in the book 1491. This above article is really scant on details.
Anyhow, the amazon basin is a humid, waterlogged region, with soils that are actually fairly nutrient deficient.
The amazonian people developed a technique to improve, dramatically, and in a long-lasting manner, the quality of the soil.
They "smoldered" wood, NOT burnt, and produced charcoal which was mixed into the earth with broken clay pottery as well as compost/manure. This produced a type of soil that, even hundreds of years after its production/use, is highly valued and productive today.
It's astounding, actually, if you read the science (I recommend reading 1491 as it covers it extensively), where yields are increased several-hundred fold, and with soil that maintains its viability for generations of continuous farming.
Essentially, by farming in a style of permaculture, with trees mixed with various crops and livestock areas this is a pretty incredible and sustainable adaptation.
I know that this amazonian dark earth aspect isn't directly attributed to being a swamp adaptation, but given the fact that the amazon basin is largely swamp/wetland area, I figure it's worth mentioning.
It's also worth mentioning the land-reclamation techniques used by the Dutch.
Dutch Land Reclamation:
Although, this is not farming in the swamp per se, it speaks about damming off regions, and pumping the water out from them. Theoretically, if your swamp and farming of it, was on such a large scale as the executed by the Dutch, you could investigate this also for your world design.