A Monmouth County man was arrested on Saturday after he got into a fight with his father, who died the following the day, authorities said. The investigation began on June 1 when officers from the Middletown Police Department were called to a Pine Street home around 6:30 p.m. for a report of domestic violence, according to a release from the Monmouth County Prosecutor’s Office. Police found two men, 36-year-old township resident Kyle Kiernan and his father 62-year-old Lawrence Kiernan, who was suffering from undisclosed injuries but refused medical treatment, the office said. Kyle was arrested…