A bizarre family agreement led to a father and son mixing their sperm because they could not afford the IVF.
The family will not have to take a paternity test after winning a High Court battle with the council.
The man, known as PQ, and his then-partner, JK, agreed to mix his sperm with his father's and inject it into the woman after facing fertility problems and struggling to afford IVF treatment, the Daily Mail reports.
After Barnsley Council heard of the strange conception in separate proceedings, it brought a legal bid over the parentage of the child.
Justice Poole concluded that the family may wish to undergo a paternity test to tell the child at a later date
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The case went all the way to the high court where Justice Poole was told that the arrangement was "always intended" to be kept secret and has led to the birth of a now five-year-old boy, known as D.
Barnsley Council had asked the High Court in Sheffield to direct DNA tests that should be carried out to determine whether the man was D's father. But in a judgment earlier today, Justice Poole dismissed the bid and ruled that the council had "no stake in the outcome."
Dismissing the council's bid, the judge said the local authority does not have parental responsibility or a "personal interest" in the boy's biological parentage.
He added that the family may wish to undergo a paternity test to tell the child at a later date "but that is a matter for them."
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Sheffield Crown Court
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Justice Poole said the man had an established father-and-son relationship with the child and it was up to him and the boy's mother to "manage the latent risks to his welfare."
"It must be acknowledged that the circumstances of D's conception cannot now be undone...Without testing, his biological paternity remains uncertain but there is a strong chance, to say the least, that the person he thinks is his grandfather is his biological father, and that the person he thinks is his father is his biological half-brother."
He added that the family's actions had created a "created a welfare minefield."
Justice Poole added: "I cannot believe that JK, PQ and (his father) RS properly thought through the ramifications of their scheme for JK to become pregnant, otherwise it is unlikely that they would have embarked upon it."
He concluded by saying that the boy "is a unique child who would not exist but for the unusual arrangements made for his conception, but those arrangements have also created the potential for him to suffer emotional harm were he to learn of them.
"[The council] may wish to know who is D's biological father, but it has no stake in the outcome of its application.
"A wish to uphold the public interest in maintaining accurate records of births does not confer a personal interest in the determination of such an application."