The name, PAJER, is of German origin. It may be connected with the 'Donauschwaben', Swabian/Bavarian German settler migrants to Hungary in the Seventeenth and Eighteenth Centuries after that land's depopulation during the extended wars of the Holy Roman Empire against the Ottoman Turks.
The Habsburg rulers offered incentives to veterans of the Turkish wars to come and rebuild Hungary. The family roots possibly go back 800 years in Bavaria/Rhineland/Pfalz.
Other (European) spellings and pronunciations of 'Payer' were Pajer, Bayer, 'Pai-err', 'Peier', and 'Pyer'.
The immediate point of emigration to the USA was Borsod-Abauj-Zemplen County in Northeast Old Hungary, of further subdivison Saros. It is possible that other Pajer family members arrived in the USA from the Eperjes (now called Presov) region of what has since become Eastern Slovakia. Other marriage related family names are the German Fuchs, Krautkremmer
(Krautkremer, Krautkraemer), Kurtz, Paumer and Schmidt; The Hungarian Marko, Toth, Wanyo (Vanjo), Gyomber (Dumbier) and Debrecenyi; The Slovak Maczko (Matsko), Dumbier (Gyomber) and Soltis; And on the wife's side the Tyrolean Rossi, Marches, (Marchese), and Salvaterra.
Research for years prior to 1700 where the data is still sparse will probably take us to Stuttgart Germany, Swabia (Schwabenland) and the Rhineland. Any connections found by others would be appreciated and what we have, gladly shared.
Source: http://familytreemaker.genealogy.com/users/p/a/y/Stephen-Francis-Payer/index.html