The family, who all hold season tickets at Bramall Lane, were hoping to take the youngster to his first ever match against Rotherham on Saturday, March 9.
However, they were told by the ticket office that, because the clash is an A* fixture, they would have to pay a child’s price of £18.
The mum, who wished to remain anonymous, branded the behaviour of the club ‘disgusting’ and accused them of trying to suck as much money from fans as possible.
She said: “My father phoned the ticket office and told them we had a six-month-old boy and we wanted to come to the Rotherham game. He was told as long as they had a ticket and brought his birth certificate it would be free.
“We went to the ticket office on Wednesday and spoke to a woman there who told us that because it was an A* game they would have to pay a child’s price.
“I can’t believe they are charging that much for a baby that will sit on my knee and he does not need a seat. Even if it was £5 it would be too much but £18 is just disgusting."
The family boast eight generations of season ticket holders and the Kiveston mum said she took her daughter to her first game when she was three weeks old.
She has called on the club to reconsider their policy but Sheffield United have confirmed that complimentary tickets for high-profile games would not be available.
A spokesman for Sheffield United said: “It is unusual that requests for tickets for children under the age of two are made, although we do offer baby changing facilities in some locations inside the stadium.
“Whilst we do offer complimentary tickets for some lower profile games, when we advise families about the issues relating to bringing very young children along, the club has a recognised, long standing policy that, for high profile A* star games such as Rotherham, that this facility is not available.”
The mum added: “It’s bizarre, they are trying to get more families in but then they are ripping them off. My son has had a difficult start to his life with family troubles so it’s taken a lot for me to build up the courage to take him.
“They are just trying to such as much money out of us as possible. They should be focussing on the supporters, treating us as if we’re family when we’re paying so much for a season ticket.
“We follow them through everything but this is still how they repay us.”