Right off the bat I can tell you no. Not in a 6 gallon, they need at least 6 friends, actually more is better, and they can get quite big (2.4in)- which is way too much for the tank.
They also like temps on the lower-mid 70's, which your betta wont.
I dont think they can live in anything under a 10-20 gallon, 10 being maybe too small, even. Their diet is a bit fickle, too.
If you want a tank mate, get a snail or two. Shrimp would be ok, but in a small tank they might become a snack. Frankly, no other fish can live in a tank with a betta under 10 gallons, except another betta in a minimum of 5.
If you get a 10 gallon, get some tetras..theyre cute like the penguins and are much easier to care for <3