*Conrad I Duke of Franconia King of Germany
born about 0890 Babenberg
died 23 December 0918 Germany

father:
*Conrad Duke of the "Old" Franks
born 0845 died 0906
or
*Adalbert of Franconia
died 0906 Theres Castle (beheaded)

mother:
*Glismut of Saxony
(end of information)

siblings:
*Mathilda von Hesse born about 0899 Hesse, Germany
Eberhard of Franconia died after 0936 Babenberg

spouse:
*Kunigunde Alaholfing Countess In Swabia
born about 0870 Schwaben, Bavaria

children:
*Kunigunde of Germany born after 0913 Speyergau
*Hermann Duke of Franconia born about 0913 Franconia
died 0948

biographical and/or anecdotal:
King from 0911

notes or source:
ancestry.com
Encyclopedia Britannica
The reason for the two fathers is that Eberhard of Franconia was definitely
*Conrad of Franconia's brother (Encyclopedia Britannica).
However they are listed under different sources as having two different fathers.
Hence the confusion.