All the candidates felt that this year's question paper was too easy.
There is nothing wrong with this sentence as it stands. This year's question paper is an ordinary noun phrase, with this year's acting as its determiner. That is idiomatic in even the most formal writing: this year's paper is the paper in use this year.
All the candidates felt that this year the question paper was too easy.
There is nothing wrong with this sentence, either, but it is not in any way superior to the first sentence. The difference is that this year is deployed as a modifier to the entire subordinate clause rather than just its subject. That means that paper now lacks a determiner, which is supplied with the.
There is, by the way, no such thing as a 'possessive sentence'. Nouns and pronouns may be possessive, but not sentences.