A transgender man wants to be listed as his baby's father or parent after being told he had to be named the mother because he gave birth to the child.
The High Court was told he was born a woman but had legally become a man by the time of the birth.
He is challenging a law which requires people who give birth to be registered as mothers.
If successful, his child could become the first person born in England and Wales to not legally have a mother.
His lawyers said a registrar told the man the law required people who give birth to be registered as mothers.
The man is accusing the body set up to administer statutory provisions relating to the registration of births and deaths of discrimination.
Forcing him to register as the child's "mother" breaches his human right to respect for private and family life, he claims.
The man, who cannot be identified for legal reasons, says such "interference" is not proportionate or necessary in the light of changes which have "evolved in society".
On Thursday, a judge heard preliminary arguments from lawyers representing the man and lawyers representing the Registrar General for England and Wales at a High Court hearing in London.
Lawyers say other transgender men have given birth but have been registered on birth certificates as mothers.
They say if the man wins his fight the child will be the first person born in England or Wales not to legally have a mother.
A decision is expected after a trial in September.