The Welsh U21 international joined Ian Evatt's side on an initial one-month loan deal last month, linking up with fellow Blades youngster Tyler Smith, and has established himself as first-choice left-back for the Bluebirds.
'Rhys is a fantastic footballer, he has done really well for us,' Evatt, the former Chesterfield defender,Â said.
'He is a proper man for 19, he copes with this level really well and has done great for us.'
The defender will miss Barrow's game this weekend away at Bromley, however, as he's away on international duty with Wales. Robert Page's U21 side face Romania in an European Championship qualifier this weekend, and face Switzerland next Tuesday.