What kind of 3 gallon tank is it? Is it an Eclipse with a bio-wheel? I have a betta in this tank, but I don't use the bio-wheel filter because the current is too much for the betta. They like calmer waters. A sponge filter with a gang valve would work (see pics in my gallery), or another small filter that would be good is a Whisper 2-10i on the lowest setting.
You could try a few ghost shrimp with the betta. When I put some in my betta tank, they didn't last long. But as the others said, YMMV
! Also, as mentioned, a 3 gallon tank is too small for a group of cories, and one by itself wouldn't do well.