Implementation of disjoint set in Java with linked-list
Nitpicks

Disjoint is a single word, your class should be named DisjointSet
The correct spelling for the &quot;sink&quot; is representative

Formatting and Style

It's generally recommended to always put braces around blocks in if-else constructs. Yes, even when they only throw an Exception.
Binary operators usually have a space on each side. (applies curr != null and xSet.rank &gt;= ySet.rank)

OOP vs. Functional-Style
Your way of writing OOP is... strange. union, append and findSet are defined as instance methods, meaning they need to be called on a certain instance of DisjointSet, but they don't actually use the instance at all.
Overall these could all be completely extracted into a static utility class, and nothing much would change. I strongly advise you to actually do exactly that. It should clarify responsibilities and make the code clearer to follow.
Alternatively you could make these functions actually start working in an OOP way. If you do that I'd furthermore suggest to make DisjointSet something like an immutable class (see String or Path) that will create a new instance when you union or append another Set to it. In fact I recommend you do that, even when you don't rewrite the code into a more OOP fashion.
Additionally your DNode's data could (and should) be declared final to avoid modification.