Jones was arrested and charged with third-degree assault, according to the police report.
Police arrested a college basketball coach Thursday after a Florida tourist, in Queens for his stepsister's wedding, died after a punch to the face.
Szabo, also 35, was taken off life support Tuesday.
A witness told Associated Press Mr Szabo may have been intoxicated and knocked on a number of vehicle windows before Jones allegedly hit him.
The coach got out, followed Szabo to the sidewalk, clocked him and sped off, police said.
Jones coached at FGCU from 2013-2015.
It's unclear why Jones was in New York City over the weekend.
The man fell to the pavement and hit his head.
Jones allegedly punched Sabor Szabo in the face at 1:15 a.m. ET on Sunday morning after a confrontation. The coach's next court appearance is scheduled for October 2, the Queens District Attorney's office said.
He is entering his second season on the staff at Wake Forest. He began moving through the college ranks in 2013 at Florida Gulf Coast, before stints at VCU and Central Florida.
His employers described him on Facebook as "super outgoing, friendly, and an incredibly smart businessman".
Szabo, who lived in Boca Raton with his brother, always had a bright smile and shared a love of fishing, cooking and family, the company said. "He was a really good person".
Wake Forest University tweeted a statement Thursday, saying, "We have just been made aware of this matter and we are gathering information".