Hi
According to the "Familiennamenbuch" (locating each surname to their town of origin / Heimatort), there were Aebi in the the following towns of origin in the year 1800: Affoltern im Emmental, Heimiswil, Hindelbank, Kirchberg, Leimiswil, Lyss, Oberburg, Rüderswil, Seeberg, Walterswil, Wynigen.
https://hls-dhs-dss.ch/famn/index.php
According to the CD-ROM of Paul Hostettler, there were the following proofed Täufer named Aebi:
- Äbi Durs (hinder Sumiswald, Täuferlehrer; 1670)
- Äbi Durs ("des töüfferlehrers ynzüchung"; 1670)
- Aebi Durss (Täuferlehrer, an die Grenze gestellt; 1670)
- Aebi Durss (Amt Trachselwald)
And not proofed but mentioned on another list:
- Gilgen-Äbi Hans/Elsbeth, von Schwarzenburg Stolzenmühle, Täufer mit Aufenthalt im Elsass; Sohn in Schwarzenburg ist †. Erb-fragen. 1722.
Source: Hostettler, Paul. Täufer-, Waldenser- u. Familienforschung, 1976-2009. 3. Aufl. Bern, [P. Hostettler], 2009.
I think the Äbi Durs / Aebi Durss is all the same person, just mentioned in four different sources. The was a Täufer teacher, lived in Sumsiwald (which is in Amt Trachselwald) an was sent to the Swiss boarder.
The couple would be Hans Gilgen and Elsbeth Gilgen born Äbi, town of origin of the Gilgen is Schwarzenburg, he was Täufer and was in Alsace (today's France). He had a son in Schwarzenburg who died. Possibly died in 1722, which might be the source of information, which would be a will ("Erb-Fragen")?
Paul Hostettler also mentioned this journal:
https://mennonitica.ch/mennonitica-helvetica/
I hope this helps.