It’s the fear of long words. Sesqui is Latin for one and a half, and the phrase “sesquipedalia verba” was used as long ago as the first century BCE by the Roman poet Horace, to criticise writers who used words “a foot and a half long”. Converting this into a fear of long words, should really only require us to add -phobia on the end, but the longer version appears to have been coined by the American poet Aimee Nezhukumatathil in 2000, who presumably added the extra syllables for literary effect. Like aibohphobia (fear of palindromes) this is an amusing wordplay, not a genuine medical condition.
LV