The phrase "attest its" is correct and usable in written English.
It can be used when indicating that something serves as evidence or proof of a particular fact or quality.
Example: "The results of the study attest its effectiveness in improving patient outcomes."
Alternatives: "prove its" or "demonstrate its".
At this point it is too early to attest its safety.
But his main devotion was to cricket (and, as witnesses to his flirting can attest, its players' wives).
The results of the evaluation of the methodology attest its efficiency in terms of learning degree and performance of the students.
As many who have traveled the Trans-Siberian will attest, its trains offer a rare chance to glimpse the heart of a great nation.
The latter, however, made little headway until the late 4th century, though the frescoes at Lullingstone in Kent and the mosaics at Hinton St. Mary in Dorset attest its presence among villa owners.
Secondly, as anyone who has been press-ganged into buying The Telegraph to get free water will attest, its systems are able to cope with different prices for the same item.
The city gradually declined under the Seleucid kingdom and after, its ruins attesting its ancient glory.
Yet his dynasty endured some 40 years, and archaeological evidence, from hostile witnesses at that, attests its greatness.
Though the coalition attests its financial statements were reviewed by an independent accountant, tax filings show the accounting firm was owned by Barchiesi's son.
The foundation date of the Castle of Zena are still unknown, though the first document attesting its presence dates back to 1216.
It is observed that antenna selection is able to provide substantial gains in terms of channel quality and reliability in interference-limited scenarios, attesting its suitability for large-scale femtocell deployments.
