The incident took place today in Gopiganj Kotwali area's Jahangirabad Ganga Ghat.
"Initially we were informed that the woman along with her children jumped into the river but later it was clarified that the woman had thrown her children in the river and she has accepted doing so. A search operation is underway," said Ram Badan Singh, Superintendent of Police (SP).
Search for the other four children is underway and further details are awaited.
( With inputs from ANI )