The victim suffered serious injuries after being punched repeatedly by James Eltringham during the assault at a house in Morley.
Leeds Crown Court heard Eltringham and his partner had spent the day drinking with one of her male friends after he came to visit them from London.
Adam Walker, prosecuting, said all three returned to his girlfriend's home later in the evening and continued drinking.
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The victim went to sleep on the sofa but was woken by Eltringham at 4am.
He accused him of kissing his girlfriend and began punching him in the face.
Eltringham then went upstairs and returned with his mobile phone which he claimed contained footage of him kissing the woman.
The victim denied kissing her but was punched again in the face.
The police were contacted and officers went to the property on Horsfall Street and arrested Eltringham.
The court heard the victim suffered a fracture to his eye socket and bruising to his face.
Eltringham, 45, of Kenton Lane, Newcastle, pleaded guilty to assault occasioning actual bodily harm.
Kara Frith, mitigating, said Eltringham was sorry for what he had done.
Ms Frith said Eltringham had served as a bomb disposal officer with the army.
He was based in Iraq until 2014 and had mental health issues as a result of his experiences in the forces.
Ms Frith said: "This is an unprovoked and unpleasant attack.
"There is absolutely no justification at all for this attack and he has expressed his remorse.
"He is shocked by what he did and this has been the catalyst for him to accept that he has some mental health problems."
Ms Frith described the defendant's actions as "paranoia exacerbated by alcohol."
She added: "He believed he had witnessed the victim and his partner kissing."
Eltringham was given a 20-month sentence, suspended for 18 months.
He was ordered to pay £1,000 compensation to the victim.
Eltringham must also do 160 hours of unpaid work and complete 20 rehabilitation activity requirement days.
Sentencing, Judge Rodney Jameson QC said: "You spent many years in the army serving your country in a particularly perilous way, acting as a bomb disposal officer.
"It is apparent from what I have heard that that has affected your mental health in a way that is not entirely uncommon for veterans in that conflict."
Describing the attack, Judge Jameson said: "It was a substantial assault, causing serious injury to him, close to the borderline of causing really serious harm."