What is it called when you change a well known quote to suit your subject? [duplicate]

Solution 1:

The word I've heard used for this on the linguistics blog Language Log is snowclone (it's derived from phrases of the format "If Eskimos have N words for snow, X surely have Y words for Z.")

Here's a Language Log post that describes the moment the word was coined and that links to some examples: Snowclones: Lexicographical Dating to the Second

And here's how it's defined by Collins Dictionaries online:

a verbal formula that is adapted for reuse by changing only a few words so that the allusion to the original phrase remains clear

You might also be interested in looking at the answers to the following questions:

• This book will change your wife – trope?
• Is there a general name for this: “The more you X the more you'll Y”
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Solution 2:

I think you are looking for 'to paraphrase':

• The adaptation or alteration of a text or quotation to serve a different purpose from that of the original.

(AHD)

Solution 3:

"Paraphrasing" was already offered, so I'll suggest something more colorful like "hijacking" or "co-opting".