The bastardy bond was received today for Jane Leeson. She named the father of the child she had, born on the 1 Jan 1815, as Henry Watson. Unfortunately she did not list the name of the child on the bond.
The baptism of Joseph Leeson born to Jane Leeson was on the 4 Jan 1815 in Packington, so this matches the birth date listed. Jane later married John Willson 5 years later and had other children, the boys were brickmakers, an occupation that the Henry Leeson I am researching also had. As for a Joseph Leeson, I have not conclusively found one that fits, hence the doubt if his name was correctly recorded.
Unfortunately the documents I have all show the Henry I am looking for a as born 1815 but none has the exact birthdate. If it was proved that Henry was born on the 1 Jan then I would assume that the name on the baptism was an error. However, without that proof, it is a theory.
Thanks everyone for their help to date.