Questioning adverbs are provided in this article. The words listed here are commonly found along with the verb questioning in sentences. This reference page helps answer the question what are some adverbs that describe or modify the verb QUESTIONING.
closely, constantly
continually, critically
eagerly, openly
really, seriously
Hope this word list had the questioning adverb you were looking for. In addition to adverbs used with questioning, other example verb adverb pairings can be found on this site.
You can help by adding more adverbs in the comments. Thanks.