Perhaps

google

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late 15th century: from per + hap1.

wiktionary

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From Middle English perhappes, perhappous, variant of earlier perhap(“perhaps, possibly”), equivalent to per +‎ hap(“chance, coincidence”) +‎ -s.

etymonline

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perhaps (adv.)

"possibly," late 15c., perhappes, with adverbial genitive, from earlier perhap (mid-14c.), from per, par "by, through" (see per) + plural of hap "chance" (see happen), on model of peradventure, perchance, etc. which now have been superseded by this word. Perhappons "possibly, by chance" is recorded from late 15c.