Barclays was the second sponsor and the first sponsor was Carling from the 1993/94 season (there was no sponsor for the first season) to 2001/02 season when the titile sponsor changed from Carling to Barclays.
The linked EPL history on premierleague.com states
Apart from the opening campaign in 1992/93, every season of the
Premier League has had a title sponsor. From the 1993/94 season,
England’s top flight was known as the FA Carling Premiership, before
the sponsorship changed in 2001 to Barclaycard until 2004.
The title of the competition then changed to the FA Barclays
Premiership, with this being amended to Barclays Premier League ahead
of the 2007/08 campaign.
Season 2015/16 marked the final campaign of a title sponsor
arrangement, with the competition name becoming Premier League from
For more information, you can read Carling on premierleague.com.