Hap, n.
Etymology: [Icel. happ unexpected good luck.
That which happens or comes suddenly or unexpectedly; also, the manner of occurrence or taking place; chance; fortune; accident; casual event; fate; luck; lot. Chaucer. Whether art it was or heedless hap. Spenser. Cursed be good haps, and cursed be they that build Their hopes on haps. Sir P. Sidney. Loving goes by haps: Some Cupid kills with arrows, some with traps. Shak.
3 other Webster entries under this spelling
Hap, v. t.
To clothe; to wrap. The surgeon happed her up carefully. Dr. J. Brown.
Hap, n.
A cloak or plaid. [O. Eng. & Scot.]
Hap, v. i.
To happen; to befall; to chance. Chaucer. Sends word of all that haps in Tyre. Shak.
Shades of meaning
Fernald has no entry of its own for hap; he lists it under accident.
He lists it without comment; the entries above explain its neighbors.