Testimony included a friend of Williams who said he confessed to killing the Somerset County Sheriff's Office deputy.
"He told me that he had shot Gene," Chris Williams told the jury.
Somerset County Deputy Isaac Wacome also testified that he and Corporal Cole were looking for John Williams to arrest him on drug charges in the hours before the shooting.
Prosecutors say Williams shot Cole in retaliation for arresting his girlfriend a few days beforehand.
The defense team says Williams was too high on drugs to intend to kill the deputy.
Justice Robert Mullen said the two-week trial is progressing faster than he expected.