Appositives with possessiveness?

Solution 1:

Yes. That's right.

The possessive -'s suffix has gone from being a paradigmatic Genitive Case suffix that marks the possessor noun in Old English (or Modern German), to being a syntactic clitic marker in Modern English that marks the end of a Noun Phrase containing the possessor (e.g, the King of England's mistress).

Since the boy and Adam are both noun phrases in an apposition relation, that in itself constitutes an NP, and that NP ends with Adam. Hence that's where -'s may be placed.

The boy, Adam's, favorite toy was a bike.

However, -'s may also mark both of the apposed NPs, since they're NPs too, and they're both possessors.

The boy's, Adam's, favorite toy was a bike.

In writing, this last construction might be a good occasion to use a dash to set off the appositive.

The boy's -- Adam's -- favorite toy was a bike.