Three gal is a lot more than the pico tanks I have aroun d here are, and they all have had fish in them since they were cyled, some being over two years now. I keep yellow clown gobys, neon gobys, yellow watchman gobys, in them all with no problems. I kept a small pink skunk clown in a 2 gal for close to a year. It was in my larger 110 gal tank for over two years and it was still just a small fish so I figured heck why not, and he did fine in that pico tank.
Any of the symbiotic gobys along with a pistol shrimp makes a good pair ina small tank as such, and the yellow watch man as is the yasha hasha goby both good to pair up with a pistol shrimp.
Or yu can get a panda goby which is supposedly the smallest fish. I have one and its only about 1/2" long, and it lives in a 3 quart Aqua Vase and does just fine. They are kind of pricey though. I paid $45 for mine.....