Quoted Possessives Ending in "s"
No style guide has shown how to write the possessive of a quoted title.
Therefore, you have three options.
Option 1: Recast
Instead of using possessive apostrophes, just write:
The cast of "The Sopranos"
Option 2: Italicize
Instead of quoting the names, just italicize them (even though it may not align with style guides):
The Sopranos's cast
Note: "The Sopranos" is singular, not plural. Therefore you add an apostrophe + "s" to make it plural.
Option 3: Improvise
It isn't in the style guides, so you can do whatever you want! Do whatever is the most logical to you.