The problem with keeping a betta with a fish under an inch long is that
a) Betta can and do eat fish of this size. If you don't believe me, just ask my endlers livebearers :/
b) I cannot think of a single fish below about 1.5 inches in length that is not a shoaling fish or at least social. And I know my nano fish lol!!! Any tetra, danio, pygmy cory or rasbora has to be kept in a group of at least 6 and small livebearers, killies and dwarf frogs need a minimum of 2 buddies of the same species. Smaller creatures have evolved to stick in groups to stay safe and it is really hard to find a small fish that does not conform to this rule.
I would say the smallest possible setup in which your betta could have a tankmate would be a 3 gallon with a zebra snail or 3 or 4 ghost shrimp. You might have to clean it twice a week however.