Q:

What are some tropes associated with social acceptance or rejection of infants with supernatural abilities?

Are there any tropes regarding how societies react to children with supernatural abilities, besides abandoning in the woods or, for the complete opposite, considering them gods? Is there anything between those two extremes?
I'm working on a story where 2% to 4% of children are born with supernatural abilities, present at birth. 
Obviously, stories about overpowered babies are as old as dirt, and tropes about such children are equally common. But while TV Tropes has "Goo Goo Godlike," "Enfant Terrible," and even "Fetus Terrible," it's harder to find any tropes regarding how societies react to such children beyond either abandoning them, Romulus and Remus style, or worshipping them as little demi-gods (or both, having started with the former and then being adopted by a local king).
Are there any alternative tropes out there, or am I really restricted to working with, subverting, or deconstructing just these two?

A:

Though I consider this more of a worldbuilding thing, I do find it too fascinating to pass up. You see, you highlight the two potential camps where people might fall into:

abandoning in the woods
considering them gods

But these are views on them. There might be a more nuanced look. If you consider 'supers' in The Incredibles, for example. 

(above is a picture of Mr Incredible, Frozone, and Syndrone, from The Incredibles)
You are basically put in the same black and white picture: good versus evil, us versus them. This is, in itself, a trope you can subvert if you get creative (or follow George RR Martin in offering more nuance).
Like showing more about a culture surrounding it. With The Tyke Bomb (also TVtropes, be warned). In which you have a group, though typically an 'evil' group, raising these children and indoctrinating them from youth into their organization. You can toy with that quite a bit (religion's pros and cons, army and patriotism)
Or maybe toying with more common tropes like The Fetus Terrible (also TVtropes). You can toy with the 'devil's baby', or demonic offspring expectation. But this has been done. I mean, I've read a lot about 'the son of the devil' stories, who both follow (Constantine) and reject (Blue Exorcist) their biological father. 
People might (rightly) be fearful of the children (or even fetuses) and consider them to have the Face of an Angel, Mind of a Demon. Or they might well be the Goo Goo Godlike you mentioned.
So there are plenty of tropes to consider, but more importantly, you just need to consider what people might well believe in their 'natural' surroundings. So it really boils down into what you want to consider.

