He is implied based on his illegitimate son's real surname being revealed in the 1857 census. He and Elisabeth never married. No additional information is available at this time, although there were numerous Schneiders living in Grimm, so there are lots of possibilities to look at when searching for his father.
The most likely father, however, probably came from the Schneider family that lived closest to the Kobers:
Household #270 in the 1857 census
Household #242 in the 1834 census
Of the possible fathers, three brothers, only two of them may be a match to the Mr. Schneider of this profile:
Johann Georg Schneider, born 1797
Jakob Alexander Schneider, born 1803
Third brother Johann Tobias Schneider, born in 1796, died two years before Georg Konrad was born. If his birth year is off by a year, then its possible he fathered Georg Konrad but died prior to his birth.
Head of the Household Michael Kober, age 78 in 1816, deceased 1824
Child #1 Philipp Michael Kober, age 47 in 1816, deceased 1824
Grandchild#1 Johann Friedrich Kober, age 20 in 1816, to household #299
Grandchild #2 Georg Konrad Kober, age 19 in 1816, to household #299
Grandchild #3 Johann Philipp Kober, age 33
Wife of Grandchild #3 Maria Barbara Kober, age 32
Grandchild #4 Tobias Kober, age 30
Wife of Grandchild #4 Anna Louisa Kober, age 36
Great Grandchild #1 Maria Elisabeth Kober, age 5
Great Grandchild #2 Philipp Jakob Kober, age 2
Great Grandchild #3 Johann Konrad Kober, age 6 weeks
Grandchild #5 Georg Konrad [Schneider], age 16, illegitimate grandson by daughter Elisabeth
In the 1857 census, his son Konrad is the surviving son who took over his stepfather's household after his death. His son is listed as Child #1 in the census entry below.
Head of the Household Philipp Kober, age 49 in 1850, deceased 1851
Child #1 Konrad Schneider, stepson, age 39, wife's illegitimate son
Wife of Stepchild #1 Katharina Elisabeth Schneider, age 37
Grandchild #1 Christina Margaretha Schneider, age 19
Grandchild #2 Philipp Michael Schneider, age 16
Grandchild #3 Philipp Jakob Schneider, age 13
Grandchild #4 Johann Heinrich Schneider, age 10
Grandchild #5 Anna Margaretha Schneider, age 8
Grandchild #6 Katharina Elisabeth Schneider, age 6
Grandchild #7 Georg Karl Schneider, age 2 years 6 months
Brother of Philipp Kober Tobias Kober, age not noted but born about 1804 according to 1834 Grimm census, deceased 1857
Child #12 Philipp Jakob Kober, age 28
Wife of Child #12 Helena Katharina Kober, age 28
Grandchild #8 Louisa Kober, age 5
Grandchld #9 Christina Kober, age 3
Child #13Johann Konrad Kober, age 25
Sources
↑1834 Census of Grimm in the District of Saratov, Russia, Dated 2 February 1835, Revised Edition; Translated by Brent Mai, Concordia University, Portland, Oregon; Published by Dynasty Publishing, Beaverton, OR, USA; Copyright 2011; page 75, family #252.
↑1857 Census of Grimm in the District of Saratov, Russia, dated 5 November 1857; Translated by Brent Mai, Concordia University, Portland, Oregon; Published by Dynasty Publishing, Beaverton, OR, USA; Published 2005; page 102, family #280, Philipp Kober family.
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