220I looked through the index to baptisms from 1826 to 1852 in the parish of Celle-Stadt on archion and was able to identify the following Speckhan births: 
 
Speckhan, Dor. 1832, 690/279 - illegitimate child of Marie Speckhan and Jüdel, lawyer in Celle, originally from Hannover, child born 26 November 1832

Speckhan, Adolf 1834, 197/191 -  illegitimate child of Marie Speckhan und Heinrich Rickmann, brick mason journey man, born 26 Juni 1834, witness Adam Speckhan

Speckhan, Johanna 1840 133/285 - illegitimate child of Dorothee Speckhan and Heinrich Krone, born 07 Nov 1840

Speckhan, Dor Mar 1845, 616/276 - illegitimate child of Marie Elisabeth Speckhan and Carl Rode, railway worker, born 18 okt 1845

Speckhan, Louise Dorothee Marie Elise 1849, 325/163, father Adam Speckhan, mother Sophie Marie Elis. Müller, born 17 April 1849, Witnesses Louise Str???, Dorothea Speckhan, Marie Speckhan, Elise Müller

Speckhan, Mar Dor 1851, 537/108, father Adam Speckhan, mother Sophie Marie Elis. Müller, born 09 Feb 1851, Paten Marie Rickmann, Dorothea Brand

Speckhan, Joh. Elis. 1852 699/287, father Adam Speckhan, mother Sophie Marie Elis. Müller, born 29 Aug 1852, Paten Elisabeth Düwel, Johanna Müller

I think Marie Speckhan who gave birth to Adolf in 1834 is the same person as Marie Rickmann, only married. I suspect she might be a sister to Adam.  
(Marie Rickmann is witness for baptism of Marie Dorothea Speckhan, dau of Adam and Sophia)