For the purposes of this answer, I am excluding non-powered vigilantes of the Shadow or Batman type. In real life, they couldn’t pull off the “badass normal” feats they do in prose, comics and films. Base-normal humans who have access to super-technology, like Green Lantern or Iron Man would be included, though there’s little likelihood such tech can exist, given what we currently know of physics and biology. Magic is right out.That leaves us with biologically advanced humans, perhaps the results of genetic engineering, and people with cutting edge technology, or some combination of the two.The government, assuming it didn’t develop the enhanced humans, nor the supertech, would do this:A.) Co-opt the superhumans. Others have mentioned the military and civilian law enforcement agencies would recruit these beings, in order to control, study, and possibly replicate their wild talents. For those who resist that,B.) Attempt to neutralize the supers. It’d buy them off, threaten them by enforcing existing Anti-mask laws and those against vigilantism. Figure you could rescue people, even if you aren’t allowed to fight crime? Join the fire department, as a job or as a volunteer. Certain types of supertech could be declared illegal, or require special permission to possess, such as the very strict US rules for owning a legal machine gun.C.) All bets are off if there really are alien, space-faring civilizations, and someone like the infant Kal-El could pass as human. Some in the government would be xenophobic, and would consider the presence of even otherwise benevolent-seeming aliens to be unwanted interlopers, if not invaders and potentially conquerors. Others would want to treat them as explorers, and try to learn as much as possible from them. Nobody will want to be on the short end of an interstellar version of the “first contact” between the peoples of the Americas and Columbus’ expeditions. If they bring a life form that acts as a fatal pandemic, or nanites that could disassemble our system’s planets, like the legendary Grey goo, then humanity may be doomed.D.) The emergence of a biologically advanced sub-set of humanity, should it become common knowledge, is likely to cause fear and even panic among the general populace. The government may want to keep the supers a secret as long as possible. In both Robert Meyers’s novel Superfolks and Moore and Gibbons’ Watchmen, strategic arms limitation talks between the superpowers are complicated by the existence of superhumans.