Jones was drafted in the seventh round out of Arkansas State in 2013. The 24-year-old appeared in 16 games on special teams last season. Barker appeared in four games after going undrafted out of Nevada in 2013.
Jones was fined, suspended and ordered to undergo educational training after tweeted his disapproval at Michael Sam kissing his boyfriend on live television in celebration of being drafted. Jones, who was reinstated in May, later said that he does not have a problem with gay people.
The Patriots open the season Sunday against the Dolphins.
- Chris Johnson