Your third type of angiosperm could be a primitive angiosperm, aka basal angiosperm. Monocots and most dicots share a common ancestor, and this primitive angiosperm diverged from that line before monocots evolved. The primitive angiosperm will have some characteristics of monocots and some characteristics of dicots.
These organisms exist. They are called basal angiosperms because they are thought to be like the primitive ancestors of monocots and dicots. A good example is order Nymphaeaceae, the water lilies.
Here is a nice table summarizing the characteristics that interest you. I found it at https://ucmp.berkeley.edu/glossary/gloss8/monocotdicot.html
For the water lilies, here are the characteristics. I labeled each with an M or D to show which category it is more like.
Embryo with 2 cotyledons fused into one (M+D)
Pollen with single pore (M)
Flower in multiples of three, or many. (?)
Leaf veins reticulated (D)
Vascular bundles scattered (M)
Roots develop from radicle (D)
Lack secondary growth (M)
So a mix of characteristics. There are other basal angiosperms but water lilies are good one for this. They are worldwide and live submerged / partly submerged in freshwater. They are wind pollinated or beetle pollinated.
Maybe since this is Worldbuilding you want something fictional. Well, purely aquatic habitats seems challenging for vascular plants. You could imagine an ancient angiosperm that somehow managed to deal with first brackish then salt water. These huge water lilies form forests like the kelp forests.