"Had I but known" is a form of prolepsis or foreshadowing

Foreshadowing

Foreshadowing or adumbrating is a literary device in which an author indistinctly suggests certain plot developments that might come later in the story.-Repetitive designation and Chekhov's gun:...

 that hints at some looming disaster in which the first-person narrator laments his or her course of action which precipitates some or other unfortunate series of actions. Classically, the narrator never makes explicit the nature of the mistake until both the narrator and the reader have realized the consequence of the error. If done well, this literary device can add suspense or dramatic irony; if overdone, it invites comparison of the story to Victorian

Victorian literature

Victorian literature is the literature produced during the reign of Queen Victoria . It forms a link and transition between the writers of the romantic period and the very different literature of the 20th century....

 melodrama

Melodrama

The term melodrama refers to a dramatic work that exaggerates plot and characters in order to appeal to the emotions. It may also refer to the genre which includes such works, or to language, behavior, or events which resemble them...

 and sub-standard popular fiction.

The foreshadowing may be distinguished between, "advance notice": for example, "'Had I but known then what I know now, I would never have set foot on Baron von Rotschnitzel's private yacht.'" or the more subtle, "advance mention": "a 'simple marker without anticipation' intended to acquire significance later in the narrative, through analeptic recovery (75).' [in other words:]...clue

Clue

Clue may refer to:* Cluedo , a crime fiction board game** Clue , based on the board game** Clue , based on the board game** Clue , based on the board game...

s"

The phrase is used to refer to a group of Golden Age mystery

Mystery fiction

Mystery fiction is a loosely-defined term.1.It is often used as a synonym for detective fiction or crime fiction— in other words a novel or short story in which a detective investigates and solves a crime mystery. Sometimes mystery books are nonfiction...

 writers, mostly female, who wrote novels characterized by the use of the "had I but known" plot in which the narrator keeps key pieces of evidence from the police, apparently for the sole purpose of prolonging their work. The HIBK school is associated with the works of Mary Roberts Rinehart

Mary Roberts Rinehart

Mary Roberts Rinehart was an American writer, often called the American Agatha Christie. She is considered the source of the phrase "The butler did it", although she did not actually use the phrase. She is considered to have invented the "Had-I-But-Known" school of mystery writing...

, specifically The Circular Staircase (1908), in which "a middle-aged spinster is persuaded by her niece and nephew to rent a country house for the summer. The house they choose belonged to a bank defaulter who had hidden stolen securities in the walls. The gentle, peace-loving trio is plunged into a series of crimes solved with the help of the aunt. This novel is credited with being the first in the "Had-I-But-Known" school."

Other members of the HIBK school include Ethel Lina White

Ethel Lina White

Ethel Lina White was a British crime writer, best known for her novel, The Wheel Spins , on which the Alfred Hitchcock film, The Lady Vanishes , was based.-Early years:...

 and Lenore Glen Offord.

The HIBK school was parodied by Ogden Nash

Ogden Nash

Frederic Ogden Nash was an American poet well known for his light verse. At the time of his death in 1971, the New York Times said his "droll verse with its unconventional rhymes made him the country's best-known producer of humorous poetry".-Early life:Nash was born in Rye, New York...

in his poem "Don't Guess, Let Me Tell You":

“Had-I-But-Known narrators are the ones who hear a stealthy creak at midnight in the tower where the body lies, and, instead of locking their door or arousing the drowsy policeman posted outside their room, sneak off by themselves to the tower and suddenly they hear a breath exhaled behind them,

And they have no time to scream, they know nothing else till the men from the D.A.'s office come in next morning and find them.

...

And when the killer is finally trapped into a confession by some elaborate device of the Had I But Known-er some hundred pages later than if they hadn’t held their knowledge aloof,

Why, they say, why Inspector I knew all along it was he but I couldn’t tell you, you would have laughed at me unless I had absolute proof."