The Jack Hampshire is now competed for by teams in the lower reaches of the restructured Bradford Premier League, along with those knocked out of the Priestley Cup first round.
Khalid Usman (4-13) and Raheel Ahmed (3-37) combined to help dismiss Gildersome for 74 before openers Richard Whitehurst (38no) and Harvey Anderson (34no) sped Ossett to their target.
They are joined in the last four by Adwalton, Buttershaw St Paul’s and Keighley.
Buttershaw chased down Azaad’s score of 203-6 for the loss of just two wickets.
Azaad’s total was built around the efforts of Imran Mahboob (86no) and Tariq Mahmood (60), but it wasn’t enough to keep Buttershaw St Paul’s at bay as Kevin McDermott hit an unbeaten 89, while Jonathan Burston (44) and Paul Carroll (33no) provided good support.
Adwalton secured their last-four spot with a 26-run win over Championship B opponents Hopton Mills.
Adwalton made a challenging 233 with Ben Garner making 72 and Dean Jackson 34 against a bowling attack spearheaded by Louren Steenkamp (4-38) and Chris Scott (4-37).
Ashley Mackereth hit a superb 106 in reply but Hopton were unable to take full advantage as Chris Priestley (4-55) and James Curtis (3-34) pegged them back.
The closest game was at East Ardsley where the home side went down by seven runs to Keighley.
Hammy Shahzad (42) and Andy Wear (39) helped Keighley to 199, with Ashley Pearson (3-30) and Dave Kibler (3-39) impressing for Ardsley.
The hosts made 192-9 in reply with Pearson making an unbeaten 39 and Scott Mullins 30 as Shahzad crowned a good personal performance by taking 4-43.
Northowram Fields, Liversedge, Crossbank Methodists and Townville will contest the second teams’ Wheatley Cup semi-finals.
Matthew Gibson (3-14) and James Ives (3-16) impressed with the ball as Liversedge dismissed Hunslet Nelson for 139, with Chris Allen (39) top scoring.
Liversedge were nudged towards victory by James Lunn (35), despite the efforts of Joe Schofield (3-17).
Conference leaders Northowram Fields kept alive their hopes of completing a league and Wheatley Cup double with a seven-wicket win over Buttershaw St Paul’s.
Dale Jones (41) and Steve Walton (34) led Townville to 196, with Zaaid Sajawal (4-24) and Ahmed Faraz (4-22) impressing for Hopton.
William Rich took 3-4 as Mills were dismissed for 85.
Crossbank complete the semi-final line up after Keighley conceded their tie.