The 11-year-old from Havant finished runner-up in his round-robin group in the southern qualifier at Chandler’s Ford Snooker Club.
Jenkins beat Jacob O’Brien, from Leicester, 2-0 and home player Thomas Devine 2-1 but lost 2-1 to Londoner John Donovan.
It was the first time Jenkins had entered this event.
He won the club qualifier on home tables at Waterlooville Sports Bar last month and will now travel north in May for the national last-16 knockout.
World Snooker coach Tim Dunkley, who runs the junior leagues at the sports bar, has always rated Jenkins.
He said: ‘It’s important to remember that Owen is only 11.
‘A high break of 54 in competition at that age is pretty good.
‘I would love to see him knuckle down now and start taking the game a bit more seriously.
‘He needs to practise the right things, tighten up his technique and enter more events like this if he wants to fulfil his undoubted potential.’
Earlier this year, aged 10, Jenkins became the youngest Cuestars Under-21 Bronze Tour rankings champion in the 10-year history of the regional circuit.
And he is the reigning champion in his club’s Monday and Wednesday junior leagues.
Jamie Wilson pocketed £50 for reaching the final of the fourth leg of the Frames Sports Bar Championship Tour.
The 16-year-old pushed Surrey-based rankings leader Sean Harvey, who has now won all four of these Cuestars events this season, to a fifth-frame decider.
Wilson climbed to second place following the tournament at Salisbury Snooker Club.
Ryan Kneller won the top group in the Monday Junior Snooker League at Waterlooville Sports Bar to draw level on points with new Division 1 leader Jenkins.
Keira Hiscock was unbeaten in the six-strong second group and heads Division 2.
Harry Wilson and George Laxton recorded the two highest breaks in the Wednesday Junior Snooker League.
But they both lost those particular frames.
Wilson made a 32 in his defeat by second-group winner Ryan Wilson and Laxton compiled a 24 in his defeat by Finn Kirby.
Samuel Laxton was unbeaten in the top group and stretched his Division 1 lead over Jenkins to seven points. Kneller heads Division 2.
A couple of shock results led to a rare four-way tie in the Junior Pool League.
Keira Jackson beat two-time champion Rhys Pearce in a best-of-three and Kacie Keens defeated Division 1 leader Harrison Heath.
It means Heath retains his one-point advantage over Pearce, while Jackson moves up to third at the expense of Hiscock. Jake Daffin heads Division 2.