Edit: Misinterpreted your post. You would need to set up a very complex terrain set for this. You might have better luck with Wang tiles, depending on how your tiles are set up. In either case, each of A, B, C, and D is essentially its own terrain, and the “missing” interactions would create a constraint on Tiled to place them in that arrangement. It should be doable (depending on your exact tile set) but it isn’t easy.
Original post, where I thought you meant you just had a 2x2 flat terrain pattern but everything else worked 1x1:
This can be done with Wang tiles for sure, and would probably be less error-prone if you’re looking to quickly fill in large areas with this pattern and aren’t dealing with complex interactions between this meta-terrain and other terrains.
With the terrain tool, you’d need to use three terrains for this, I think, so that “A” has e.g. pattern 1232 (clockwise from top left), “B” has pattern 2123, “C” has 2321, and “D” has 3212. It might still be a little buggy when just painting with this though, since all the sub-terrains won’t have complete sets of interactions with each other.
Another, perhaps simpler, possibility is to use an interim tile for your terrain work (e.g. just “A”) and then fill all “A” with the ABCD pattern using the Fill tool. If your tileset doesn’t let you easily select ABCD as a 2x2 chuck, you can create a Stamp out of it and use that.