What is a corresponding adverb for insist?

There isn't a single perfect adverb that directly corresponds to "insist." "Insist" is a verb, and while adverbs modify verbs, they don't always have a one-to-one correspondence.

Here's how you can express the idea of "insisting" using adverbs:

* To emphasize persistence: *adamantly, stubbornly, firmly, resolutely*

* To emphasize strong belief: *strongly, forcefully, emphatically, vehemently*

* To emphasize a demand: *urgently, demandingly, imperatively*

The best choice depends on the specific context and the meaning you want to convey.