I have been doing a complete census research for the New England, Middle Atlantic states on this family, presently searching VA and WV.
Spellings found to date - Paeth, Paith, Paitt, Payte, Peat, Peate, Peats, Peatt, Peatte, Peattie, Peayatt, Peaytt, Peeyatt, Peit, Peot, Peott, Peyatt, Peyott, Piat, Piatt, Piatte, Piet, Pieth, Piette, Piot, Piott, Poitt, Payette, Payte, Pyat, Pyatt, Pyatte, Pyeth, Pyett, Pyette, Pyot, Pyott. Same are related, some possibly related and some not related. If stuck on your family, maybe you would like to try one of these spellings.