Which is the correct wording?
patent claims drafting
drafting patent claims
A: Drafting patent claims is a difficult task.
B: Patent claims drafting is a difficult task.
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"Patent claims drafting [...]", or - slightly better - "patent-claim drafting [...]" (hyphenated; singular) is grammatical, but not idiomatic. I'd argue for the latter, because you're treating "patent-claim" as an adjectival phrase applied to the gerund "drafting". There might even be an argument for "patent-claim-drafting". Consider the phrases "raising horses" and "horse-raising" for more insight as to why.
In general, you want "Drafting patent claims [...]" for sentences like your example. To a native speaker, it scans more naturally.