Who are the fertile males in ant colonies?

Male ants are not workers or soldiers. The workers and soldiers are all females, so generally when you see an ant you can call it "she". In fact they are good for nothing but mating with the queen so that she can lay eggs that will produce new queens and workers (and soldiers if it is a kind of ant that has a soldier caste; not all ants do have special soldier and worker castes). She does not need to mate to produce new male eggs, but before she can do so, she must produce enough workers to run the colony, so it come to the same thing.

However, in the proper season colonies of most ant species will produce eggs that they raise into winged ants. Most kinds of colonies produce a mix of winged male ants and winged female ants, but some kinds will produce only one sex in each colony at a time. That way, when all the ant colonies in a district send out their winged males and females, they do not mate with their sisters or brothers.

Of the female ants in most species only the young queens that are to lay eggs have wings, compared to the thousands of workers and soldiers. All males have wings.

Generally the winged males do not live long after mating, and the females mate only once. Afterwards females of most species drop their wings and spend the rest of their lives in the colony underground or wherever their nest might be.