The incident took place in Kanshi Ram Awas Vikas colony near Eidgah under Sungarhi police station.
According to reports, neighbours heard the couple screaming at each other on Friday night and when they went to the couple's house, they found the baby dead.
One of the neighbours informed the police and took charge of the body and sent it for post mortem, the report of which is awaited.
According to the husband Mohammad Shaqir, he had gone to the market on Friday evening and when he returned, he found the baby dead. His wife Phool Bi was sitting besides the dead baby.
He alleged that Phool Bi was mentally disturbed and had killed their daughter by strangling her. Phool Bi denied the allegation and claimed that her husband had killed the baby.
Rajesh Kumar, SHO, said police were waiting for the autopsy report and further action in the matter would be decided on the basis of the report.
Meanwhile, a neighbour, Bablu, told reporters that he had offered to adopt the baby as the parents were poor and were incapable of taking proper care of the newborn.
Shaqir, a rickshaw puller, was an alcoholic and spent most of his daily earnings on liquor. Shaqir had demanded Rs 15,000 for handing over the baby to Bablu so that he could use the money to get his wife treated for her mental ailment. Following the demand for money, Bablu dropped the idea of adopting the baby.
( With inputs from IANS )