In the UOPblog linguist Anatoly Liberman, while searching for the etymology of “bother”, offers the following comments about the possible origin of a related term, “pother”, which, unlucky, still remains obscure.
Pother appeared in English in the sixteenth century. At that time, it rhymed with mother, other, and the like. And the like is a tiny group.
The ODEE says: “…no source is known; perhaps influenced by bother.” Thus, bother was possibly influenced by pother, and pother by bother.
Skeat did risk offering a conjecture about the origin of pother. In his opinion, pother is the same word as podder, from pudder, which is a variant of the verb potter. Putter (around), potter (about), pudder, and podder are indeed variants of the same verb. In addition, we find Scots put or putt “to shove, throw, hurl,” familiar from golf, where putter is both a club and a person who putts. Finally, put ~ putt may be the same verb as Engl. put (in put in, put off, and so forth), even though one rhymes with shut and the other with soot. Apparently, pother can be related to that group if its sense “confusion” (“pottering about”) is primary and “choking smoke” secondary. But this is unlikely: the concrete sense (“smoke”) must have preceded the derivative one (again compare the history of qualm). Therefore, I think Skeat did not guess well. The origin of pother remains unknown and, for this reason, can tell us nothing about bother, another word whose history is obscure.