A court heard Lee Ingle, Wayne Hoban and Thomas Hawley carried out the attack after a wedding at the Chevin Park Country Hotel, Otley.
Jurors heard the victim was at the event with his partner and children and called a taxi to take them home.
Leeds Crown Court heard the vehicle arrived at the venue but left without picking them up.
The man then approached another cab that had been sent to collect Ingle and Hawley to ask the driver to make inquiries about what had happened to his taxi.
A dispute then broke out over the hold-up being caused to the defendants' taxi.
Ingle said to the man: "This is my taxi, I'm going to punch you."
The three defendants then attacked the man. Hoban kicked him twice in the head.
He suffered a fractured eye socket and had to have surgery after the incident.
Allan Armbrister, prosecuting, said the man still suffers problems with his sight.
Mr Armbrister said the victim had given a statement describing how he had suffered financially as the injury had affected his work.
He said: "I would never expect such violence to be used when all I was trying to do was get my children and my partner a taxi home.
"I get emotional about how unfair and pointless the whole thing was."
Hoban, 39, of Mill Croft Estate, Otley, was found guilty of inflicting grievous bodily harm and common assault. He was jailed for six months.
Ingle, 48, of Newhall Carr Road, Otley, pleaded guilty to common assault during the trial. He was jailed for 12 weeks
Thomas Hawley, 36, of Whiteley Croft Road, Otley, was found guilty of common assault. He was jailed for four weeks, suspended for two years.
He was also ordered to pay Â£500 compensation to the victim.
Lawyers for the defendants described them as hard-working family men whose families would suffer if they were sent to jail.
None of the defendants have previous convictions.
Judge Christopher Batty criticised the men for trying to portray the victim as a violent drunk during the trial.
He said: "The trial was an all-out assault on him, just like it was on the night.
"People have to understand that if they fight over taxis at night in a public place the court will not tolerate it."