Only "more minute" is possible. However, I don't think this collocation is very likely. Something is either minute or not; I wouldn't use a comparative with this adjective.
Although the comparative is unlikely with the adjective "minute", the superlative "minutest" exists. You might see it in a phrase like not even the minutest inspection would have revealed the flaw.This ngram shows that "minuter" has appeared in print, too, but it's one tenth as common as "minutest".