Expression for false assertions

Solution 1:

My first thought is protest too much which comes from Shakespeare's Hamlet. The line in Hamlet (Act 3 Scene 2) is:

The lady doth protest too much, methinks

The quote comes as a response to a question about a character in a play-within-the-play and, as one author wrote,

...the only criticism she has to offer is that the Player Queen's protestations of love and devotion sound too fulsome to be convincing even to the fatuous Player King

So, by protesting (denying or espousing something) too much, one appears to believe the opposite.

Solution 2:

You have the famous Latin saying:

Excusatio non petita accusatio manifesta:

• an excuse that has not been sought [is] an obvious accusation

More loosely, "he who excuses himself, accuses himself"—an unprovoked excuse is a sign of guilt. In French, qui s'excuse, s'accuse.

(Wikipedia)

Solution 3:

TV Tropes calls this one the Suspiciously Specific Denial.

A False Reassurance works because the speaker is being vague and non-specific enough to pull the wool over someone's eyes. A Suspiciously Specific Denial, on the other hand, fails because the speaker is Saying Too Much. This may be unintentional, such as when the speaker is panicked, is a Bad Liar, or perhaps just a little stupid.

Solution 4:

I'm not sure if this would work in the context you have in mind, but how about "the guilty dog barks first"? I think the meaning is basically self-explanatory, and you can see it is common enough to appear in 33 books in this Google search: https://www.google.com/search?tbm=bks&hl=en&q=%22guilty+dog+barks+first%22