Kidding on the square
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To "kid on the square" is to be joking, but at the same time really mean it. In this context, the square means "genuine" or "true" in the same sense as fair and square and square deal and three square meals, with an origin in carpentry, where a square is a tool used to ensure that objects are perpendicular to one another.
The phrase was popularized by Al Franken in his book Lies and the Lying Liars Who Tell Them when he describes the negative reaction of Paul Wolfowitz to one of his jokes. However, the phrase was in use for many years prior to Franken's book. The Raquel Welch movie Fathom (1967) [1] featured the phrase 36 years earlier. A character joked that Fathom was "kidding on the square." The phrase was also the name of a song by an alternative rock band, Tsunami, and appears on their 1994 record, Heart's Tremolo.