Hi, and welcome to TFF. I can't help on jawfish, but I have kept mudskippers.
There are a number of species in several genera, but the more commonly seen in the hobby will be species in Periophthalmus which attain around four inches. If you intend more than just one, acquire them together. I would suggest three or four in a 20g long. I would not recommend keeping them with fiddler crabs; mudskippers will be better on their own.
You undoubtedly know that they require "land" and water. Three or four inches of water depth would be good, with an area of "land" built of sand and/or wood. Keep the aquarium covered well; not only for warmth (the air must be warm like the water) but also to keep the mudskippers in. I had one that fed off my finger and one day it became so excited when I opened the cover that it jumped out and I had to chase it around the room.
Many of the common frozen fish foods make up a good diet; chunks of frozen squid (thawed obviously) are ideal, along with worms such as bloodworms or blackworms (live or frozen), frozen plankton, and small crickets. The food needs to be moving, which is how I got my mudskipper feeding off my finger. Initial live tubifex worms got it associating food with my appearance, and I moved up to using a small stick (a piece of broomstick works well) to move around small bits of frozen squid, etc. Before long he was on my finger.
Byron.