attest vs aver

attest and aver both are verbs.

Word	Noun	Adjective	Verb	Adverb
attest	No	No	Yes	No
aver	No	No	Yes	No

As verbs, aver is a hypernym of attest; that is, aver is a word with a broader meaning than attest:

attest: authenticate, affirm to be true, genuine, or correct, as in an official capacity
aver: to declare or affirm solemnly and formally as true

Other hypernyms of attest include affirm, assert, avow, swan, swear, verify.

attest (verb)	aver (verb)
authenticate, affirm to be true, genuine, or correct, as in an official capacity	to declare or affirm solemnly and formally as true
provide evidence for; stand as proof of; show by one's behavior, attitude, or external attributes	report or maintain
give testimony in a court of law
establish or verify the usage of