According to police, the incident took place Sunday night in Kishanganj area of the district, some 200 km from Jaipur.
"The man, Shambhudayal Suman, was a farmer and going through some financial difficulties. He was also alcoholic," a police officer said.
The officer said Suman stabbed his son Mukesh Kumar to death while the boy was asleep.
"It seems Shambhudayal was under influence of alcohol. After making sure that Mukesh was dead, he rushed to the well outside his house and jumped into it. When family members came to know about the incident, they informed police. His body was fished out with help of villagers," said the officer.
The officer added that statements of his family members were being recorded. "They said that Shambhudayal was very depressed over his financial problems," the officer said.