The phrase "averring that" is correct and usable in written English.
It can be used when stating or asserting something formally, often in legal or academic contexts.
Example: "The defendant is averring that he was not present at the scene of the crime."
Alternatives: "asserting that" or "claiming that".
The plea of the defendant to the original bill treated the bank as the complainant by averring that 'the said bank is not the holder of the note for value, and that the note was sued on in the name of the bank merely to give the court jurisdiction.
On the 2d of January, 1883, Meyers amended his supplemental bill by averring that the defendants had infringed his copyright by reprinting and publishing volume 40.
They showed it by averring that upon examination they had ascertained her to be lacking in the qualifications of a teacher, and had dismissed her accordingly.
His grand exoneration of Brian Williams, honest to God, consisted of averring that the NBC News anchor never said the following: " 'Ladies and gentlemen, I've seen martians.
Romney argued that providing rewards for illegal immigrants only encouraged more of them to come here, averring that it was time to "turn off the magnet".
The Guerrilla Girls, rather depressingly I think, seem to take this lack of progress with a shrug, averring that chauvinism is always with us - it simply takes different forms for different generations.
"Translated into yer actual English," the great man averred, "that means 'Honest sweat killed many a ponce'".
And while some wags may aver that's a good thing, we're having none of it.
Mr. Ely averred that service — extreme housekeeping — is physically demanding, with sore feet and bad knees the least of its debilitating byproducts.
For a church or movement which avers that "it sings its theology," Charles Wesley's Journal is an imperative.
Green might aver that Hastert's lying to the FBI didn't impede the investigation.
