The jump between the 1880 Census and the 1900 census is not always an easy one to bridge. Over the years I've compiled a list of over 260 various misspelled variations of this surname in federal census records. Up until Feb of this year I had great luck with a bare minimum of search parameters on ancestry.com. But with their Feb update one must now have the exact (and I DO mean EXACT!) spelling of the surname that they have indexed it under or it's all for naught. In each and every one of the 4,380 counties/parishes in all 50 states and the District of Columbia.
This surname can have any of several forms. Most common is the one where it ends in -thy but -they, -thie, -tha and simply -th are also found. Internal vowels are, as in my husband's surname, somewhat interchangeble: one census a family can be listed as Abernathy and another time they are found as Abernetha, but the spouse and children may be identifiable. Next, the leading A can and has been omitted, leading to Bernethy and Bernathie. Finally, sometimes, in some census records one finds Abana-- instead of Abern--. These are the most found variations. But there are others. As mentioned, up to 260 variations.
Before you posted your message you had checked the box to display your e-mail address on all your messages (a wise choice), so I can send a copy of that collected list of misspelled names to your email address, if you desire. But be forewarned: to cover all 260 misspelled names (some of which are decidedly un-intutive) and all states, there is potentially up to 1,138,800 ancestry search screens for you to look at and evaluate. I cannot guarantee that your ancestor's name is truly on my compiled list. It may be a unique new variation. So it won't be fast nor easy and I make no guarantees as to the accuracy of my compiled list. Not by any streach of the immagination!
But if you still want me to send the list instead of try your luck with the above hints, just let me know.