I have found the birth record for Jacob Friedrich Steigert (had the "t" at the end of his name at birth) in Haltingen at archion.de (pay site for German church records), and have uploaded an image to Jacob's profile. Jacob Friedrich was an illegitimate child, and the mother did not name the child's father.
The entry reads (in translation): "On 6 February  at 9:30 p.m. was born, and on 10 February baptised, an illegitimate boy Jacob Friedrich. The mother is Anna Katharina Steigert, the unmarried daughter of the late Michael Steigert, burgher here [in Haltingen]. Witnesses [to the baptism] are Michael Steigert, burgher here; Jacob Friedrich Walliser, unmarried son of the late Andreas Walliser, burgher here; Barbara Steigert, unmarried seamstress here; and Anna Katharina Kaufmann, the unmarried daughter of Johannes Kaufmann, shoemaker here. Recorded in Haltingen 10 February 1820 by T. Kaufmann, minister."