The incident took place late on Thursday at Bank of Baroda's Mumfordganj branch in Allahabad.
Under the Pradhan Mantri Jan Dhan Yojana, Prime Minister Narendra Modi has called on every family in the country to have at least one bank account.
At the time of the incident, hundreds of people from the weaker sections had gathered to get their accounts opened when two youth broke the line and got into an altercation with the women in the queue.
The youth opened fire, injuring three people
The spat turned ugly and the two youth retreated and brought some of their friends to settle scores. They bashed up people in the queue and one of them opened fire, injuring three.
A case was lodged with the police by the branch manager R.K. Sahu. The injured were rushed to the a hospital where the condition of one woman is said to be serious.
There were also complaints from some places that said bank employees took money to give forms to open new bank accounts. People alleged that the employees of the Avadh Grameen Bank camp here took Rs.100-300 for each form.
The matter has been brought to the notice of the bank management, a district official told IANS.
A total of 16 lakh new accounts were opened by various banks on the first day of the scheme on Thursday.