The Central Yorkshire League's premier cup competition now features the leading 16 first teams from last season and both Batley and Birstall have favourable home draws.
Carlton, who were relegated from the top flight last term, are one of four first division clubs in the competition and they visit Batley, while Birstall host promoted Northowram Fields.
Batley gained a first win of the season last week, beating Scholes by 89 runs, and they will see Sunday's tie as a good chance to make progress.
Birstall, who received a bye to the Heavy Woollen Cup second round on Monday after Shelley conceded, will also hope for two good cup runs.
Northowram have made an encouraging start to life in the top flight with two wins but they were bowled out for 87 as they suffered a seven-wicket defeat to Wakefield Thornes last Saturday.
Batley face a keen test on Saturday at Methley in the Premier Division, while Birstall target a third straight win at Wakefield Thornes.
Second division Woodkirk enter a new-look Barry Winstanley Cup, which is open to the remaining 11 first teams and some second teams.
Woodkirk have also been given a home tie, against Wakefield St Michael's A, while they travel to East Ardsley A in the league on Saturday.
Hanging Heaton's Priestley Cup tie at Yeadon is set to go ahead this Sunday (1pm). Yeadon's High Street ground was waterlogged last Sunday and with no prospect of the game starting on Monday, it was moved.
With the Bradford League keen to get the game played, if Yeadon's home game with East Bierley on Saturday does not go ahead the tie will be switched to Bennett Lane. Spectators can call Hanging Heaton (01924 461804) on Sunday to find out where the game is.
Heaton travel to Saltaire in Bradford League Division One on Saturday (1.30pm) aiming to bounce back from a 22-run defeat by East Bierley.