Claim adverbs are provided in this article. The words listed here are commonly found along with the verb claim in sentences. This reference page helps answer the question what are some adverbs that describe or modify the verb CLAIM.
actually, boldly, certainly, confidently, consistently, distinctly, easily, equally, especially
eventually, explicitly, fairly, falsely, finally, frequently, fully, generally, hardly
honestly, humbly, immediately, justifiably, justly, lawfully, legally, legitimately, merely
naturally, necessarily, openly, plausibly, possibly, probably, properly, proudly, publicly
rarely, really, reasonably, rightfully, rightly, safely, scarcely, seriously, simply
successfully, surely, truly, truthfully, typically, ultimately, usually
Hope this word list had the claim adverb you were looking for. In addition to adverbs used with claim, other example verb adverb pairings can be found on this site.
You can help by adding more adverbs in the comments. Thanks.