Cross Keys welcome Newport to Pandy Park in what will be a fiercely competitive local derby while two sides who started their cup campaign with defeats clash at the Brewery Field when Bridgend Ravens take on Cardiff.
Bedwas travel to Neath while Pontypridd take on Leinster A at Sardis Road in another eye-catching fixture and Llanelli host Gala.
Carmarthen Quins head coach Steve Williams is confident his side can get their cup campaign back on track when they meet fellow west Wales side Swansea.
They were defeated but not totally disheartened by their 44-32 loss to former champions Cornish Pirates last weekend and are up for the challenge of the All Whites.
"We performed well last week considering the strength of the opposition and the injuries to our squad," said Williams.
"It was disappointing not to get a win but we have a chance to keep our campaign alive with a local derby tomorrow night.
"Sunday's match was our first competitive cross-border game and it was a great experience for our boys but everyone loves a local derby and playing Swansea will be a lot more familiar for us. We have a young side, as do Swansea whereas Cornish Pirates were more mature and experienced.
"It would be great to see some extra support for us tomorrow night in the first of two matches against Swansea, first in the British & Irish Cup then away in the Premiership."
Former Wales lock Williams is relatively happy with his side's progress so far this season but believes there is more to come.
"We haven't started this season as well as we finished last season but we have had some good wins and we can only learn from the little mistakes we've made," he added.
"We're not quite there yet but we are giving young boys an opportunity and they have taken their chances well."
Cross Keys will be looking to bounce back in their clash with Newport after they suffered a heavy defeat at Newcastle last week.
Greg Woods' side were easily beaten 52-5 by the English Championship side but he believes a local derby is the perfect opportunity for his side to get back on track.
"Newcastle away was one of the toughest games we could have had first up," he said.
"We've got Newport now which is a fantastic fixture for us as it's a Gwent derby which always adds excitement to the fixture."
Elsewhere, Bridgend will be hoping home advantage helps them to victory over Cardiff as they recover from a heavy defeat to Ulster last weekend. Ben Rose's side pushed the Irish side all the way but a poor final quarter saw them eventually fall to a 49-19 defeat.
Cardiff meanwhile were beaten 23-14 by rivals Bristol at the Arms Park last weekend. The Blue and Blacks have already tasted victory at the Brewery Field this season, winning 38-11 win in the league earlier this season and head coach Martyn Fowler will be hoping for a similar result in Saturday's clash.
In Pool Two, both Bedwas and Neath will be looking for their first wins of the competition when they clash at The Gnoll.
Bedwas wing Rory Budina goes into the game on the back of two tries in his side's defeat to Bedford last weekend and will be a significant threat to the Neath defence.
The Welsh All Blacks meanwhile have been struggling of late with coach Pat Horgan hopeful his side can soon get back to winning ways.
"This week is our chance to put things right," he said.
"It's not as if the players don't know what to do but collectively we have fallen apart for the last couple of weeks and we need a win.
"We know Bedwas will be competitive as they always are but I'm not concerned about what competition it is we're playing in. I want to win every game we go into and we need to win this game on Saturday."
In the other games taking place this weekend, Pontypridd take on a Leinster side who had too much for Leeds Carnegie last weekend.
Dai Flanagan secured a draw for Ponty in their clash with Jersey but will be hoping his side can go one better on Saturday. Llanelli, who lost 36-26 at Moseley, will be hoping for a better result at home to Gala.
The remaining two fixtures for the Welsh clubs see Aberavon face a difficult trip to Ireland to take on last year's winners Munster A in Pool Seven while Premiership leaders Llandovery face an away trip to Scottish side Melrose.
British & Irish Cup fixtures:
Fri 19th Oct 12 19.15 Carmarthen Quins v Swansea
Sat 20th Oct 12 13:00 Munster A v Aberavon RFC
Sat 20th Oct 12 14:00 Pontypridd v Leinster A
Sat 20th Oct 12 14:00 Melrose v Llandovery RFC
Sat 20th Oct 12 14:30 Bridgend v Cardiff Rugby
Sat 20th Oct 12 14:30 Neath v Bedwas
Sat 20th Oct 12 14:30 Cross Keys RFC v Newport
Sat 20th Oct 12 16:30 Llanelli v Gala