Do you mean you have bought this birth certificate
IMMS, EDWARD HARDEN
GRO Reference: 1845 M Quarter in ST. MARY NEWINGTON Volume 04 Page 359
And it has father as William while the marriage of Edward has father as a James Frederick - which I can see it does, As does the late baptism.
Where are they in 1851?
Added…and what is the occupation of William on the birth certificate, and where were they living?