identify this movie - Psychological thriller in which the verse "My father was a penny" keeps recurring on a wall?

I think the phrase that you're looking for is "My daddy is a dollar / I wrote it on a fence / My daddy is a dollar / not worth a hundred cents."

I am pretty sure this is the movie because this is what the killer keeps on writing on the asylum. The movie is In Dreams and I think its very much similiar to the type of the movie you mentioned about. It has the same scene where killer when he was a kid escapes the asylum in the disguise of a nurse who works there.

Here is the youtube trailer. Hoping this is the one you are seeking.

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