The girl had a narrow escape in the firing incident as the bullet grazed past her body, causing a minor injury, police said.
The incident was reported to the police at around 8.30 PM from Madangir Market.
The accused fled from the scene leaving behind the weapon used in the crime.
Police have seized the pistol and are trying to nab the accused.
A case of was registered against him under relevant sections of the IPC and the Arms Act at the Ambedkar Nagar police station.
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When the woman protested, the youth got into an argument during which he pulled out a pistol and fired at her from a close range.
"The bullet grazed past her body and hit a wall behind her. Hearing the gunshot some locals rushed towards the crime scene but the accused managed to flee. He dropped the pistol in a hurry," a senior police officer said.
The woman was taken to a nearby hospital from where she was discharged after preliminary medical treatment.
They had recently separated due to personal issues.