What is the correct spelling of "X, schmX" to indicate dismissiveness (e.g., "evidence, schmevidence")?

There is a curious construct in American English in which a word is stated and then repeated with the prefix "schm-" or "shm-" in order to indicate the speaker's dismissive attitude toward a concern that somebody else has. For example:

"Smokers have lower life expectancies? Correlation, schmorellation—I'm going outside for another cancer stick."

Is the commoner or more "correct" spelling "shm-" or "schm-"? Is this construction used outside the US? What is its origin?

Solution 1:

This is called shm-reduplication:

Shm-reduplication is a form of reduplication in which the original word or its first syllable (the base) is repeated with the copy (the reduplicant) beginning with shm- (sometimes schm-), pronounced /ʃm/. The construction is generally used to indicate irony, derision or skepticism with respect to comments about the discussed object:

He's just a baby!
"Baby-shmaby". He's already 5 years old!

Per Wikipedia, both shm- and schm- constructions are acceptable. The TV Tropes entry is interesting as well.