A former New York City police officer displayed a mix of defiance and tears on Friday as he begged a judge not to send him to jail for falsely saying he witnessed a drug sale and for arresting an innocent man.

The former officer, Isaias Alicea, proclaimed his innocence, despite having been convicted in May of 10 felony counts of filing a false instrument, and spoke through tears about his difficulty supporting his family since he was fired.

“I’m a good dad to my 3-year-old daughter, and I’m engaged,” Mr. Alicea said. “I had truly nothing to gain from this, and I’ve lost so much already.”

Justice Patricia Nunez, of State Supreme Court in Manhattan, sternly rebuked Mr. Alicea and sentenced him to six months in prison, as a prosecutor had requested.