“Didn’t you hear me? A bride, Cinder. As in, a princess.”
“As in, not going to happen. He’s only, what? Nineteen?”
I looked it up, and it seems to mean "for example" or "such as"; but here, I believe it could mean "maybe" or "possible".
"As in" is a slang-y equivalent to "in other words" or "to say it a different way".
She's ridiculously smart, as in, a complete genius.
It's a totally new technology, as in, "you shouldn't buy it at any price". Wait at least until they've patched all the bugs.
In your example Cinder repeats "as in" to sarcastically refute Peony, by restating what she said as a contrary opinion.
Here the phrase simply means to be more precise, or in the sense of.
Didn’t you hear me? A bride, Cinder. More precisely, a princess.
I think you meant it in the sense of, not going to happen. He’s only, what? Nineteen?
The second person apparently speaks with a sarcastic tone.
Originally, "as in" was used to resolve an ambiguity by citing a phrase in which the word appears: "He was vulgar, as in 'a vulgar joke'": that is to say "I am using the adjective 'vulgar' in the way that it is used in the phrase 'a vulgar joke', and not as it is used in the phrase 'the vulgar name of a plant'".
By extension, the meaning of the word could be explained by reference to a phrase in which it does not actually appear: "She was big, as in 'obese'".
Your example, "A bride, as in 'a princess'" suggests to me "By that I don't just mean she's getting married. I mean she's living a Disney fairy tale". But I might be wrong: context is everything!
For the second example "As in, not going to happen", I think I would need to see the preceding sentence to understand exactly what it means. Perhaps: "An asteroid strike is unlikely. As in, not going to happen". Meaning "it's highly improbable, sufficiently improbable that you can work on the assumption that it's not going to happen."