Misterton Girls lost 2-1 to Carlton Ramsden Girls, in their first outing, despite leading through Eleanor Hopkins.
But they earned their first points with a 4-2 defeat of Ordsall when Jodie Clark, Lauren Smith and Frances Mallatt joined Hopkins in the goals.
East Markham, runners-up in the County Championship last season, eased to victory over Gamston.
Bassetlaw’s representatives in this year’s competition on Saturday will be Redlands Girls who won 3-1 against Ryton Park, Ellie Newton and Leah Marshall scoring.
This week’s Parry Cup quarter-finals: Langold Dyscarr v Prospect Hill ; Kingston Park v Carr Hill ;St. John’s v St.Anne’s; Gateford Park v Sir Edmund Hillary.
The Bassetlaw Boys squad for a five-a-side tournament on Friday and a game against Scarborough Boys on Saturday is: Christopher Hilbert (Leverton); Owen Bloomer (Ramsden);Corie Cole (Ryton Park); Jack Garsden, Luke Morris, Kian Smith, Jasper Dennison (Prospect Hill); Finlay Watt (Misson); Alex Pickering (East Markham); Riley Garfitt, Byron Bates (St Anne’s); Bradley Charlesworth, Oliver Goose (St John’s); Bradley Fong (Sir Edmund Hillary).