The story
Coined 1935, by Damon Runyon. Phonology pseudo-Greek – note the ph. The term may be analyzed as *phe- + dinkus (“contrivance (slang)”), where the prefix is an optional consonant /f/, with the stressless vowel added in the same way as other mutually apophonic prefixes (when the consonant changes, the vowel changes accordingly) such as pi- (pizazz), she- (shebang), etc.
Etymology from Wiktionary, CC BY-SA 4.0.