Phil Salt captains the side in Southampton in the absence of injured skipper Jos Buttler.
The T20 series is followed by five one-day internationals against the same opposition, with England picking youthful squads after relinquishing their T20 and 50-over world titles over the past year.
Essex's Cox was the top-scorer for men's champions Oval Invincibles in this year's Hundred competition while Barbados-born Bethell impressed for Birmingham Phoenix.
Surrey all-rounder Overton, who has played one Test for England, will play as a batter only as he recovers from a back injury.
England team:
Phil Salt (capt, wk), Will Jacks, Jordan Cox, Liam Livingstone, Jacob Bethell, Sam Curran, Jamie Overton, Jofra Archer, Adil Rashid, Saqib Mahmood, Reece Topley
