The warden at the time believed sex could be used to compel black men to work harder in the fields, according to a history on the practice produced in the 1970s by Tyler Fletcher, who founded the department of criminal justice at the University of Southern Mississippi in 1973. So black prisoners were allowed time on Sunday with spouses or, more often, prostitutes.

By the 1940s, makeshift lean-tos and shacks built by inmates for the visits gave way to formal facilities, and white inmates were more likely participants than black ones.

Announced in December, the decision to stop the hourlong conjugal visits came as a surprise to the handful of prison spouses who rely on them. Several have taken to Facebook and other online forums and written to lawmakers to try to save what they say is an essential part of their relationships. A Mississippi prisoners’ advocacy group and a Memphis-based civil rights organization have planned a rally for Friday in Jackson, the state capital, to protest the policy change.

But State Representative Richard Bennett, Republican of Long Beach, wants the practice stopped, and he said no amount of protest would change his mind.

He said he learned about conjugal visits a few years ago when an elementary school principal told him a student of hers had shown up with a photograph of a new sibling. The student’s mother was incarcerated. The baby had been conceived during a conjugal visit.

In 2012, Mr. Bennett introduced a bill to end the visits. It did not get much attention, so he will try again when the Legislature meets this month. He said he was aware of Mr. Epps’s plans, but wanted a permanent ban. Officials have not offered any figures on the number of babies born or the program’s cost.

“I don’t think it’s fair to the children conceived and to the taxpayers,” he said. “You are in prison for a reason. You are in there to pay your debt, and conjugal visits should not be part of the deal.”