Deserved adverbs are provided in this article. The words listed here are commonly found along with the verb deserved in sentences. This reference page helps answer the question what are some adverbs that describe or modify the verb DESERVED.
actually, amply, certainly, clearly
definitely, eminently, entirely, equally
fully, hardly, justly, probably
really, richly, rightfully, rightly
scarcely, surely, thoroughly, truly
undoubtedly, wholly, worthily
Hope this word list had the deserved adverb you were looking for. In addition to adverbs used with deserved, other example verb adverb pairings can be found on this site.
You can help by adding more adverbs in the comments. Thanks.