Midfielders Payne (illness) and Weston (thigh) as well as striker Kedwell (hamstring) all missed Tuesday's Johnstone's Paint Trophy defeat at Crawley but have recovered in time for the weekend.
Defender Fish, meanwhile, was forced off after just 13 minutes nursing an Achilles complaint but is also expected to be okay.
Allen made six changes for the narrow 3-2 defeat to League One Crawley and faces plenty of selection decisions ahead of the trip to Underhill, although goalkeeper Stuart Nelson should return between the sticks.
Allen first managed Barnet between 2003 and 2004 before leaving to take over at Brentford.
He returned again in March 2011 on a deal until the end of the season but parted ways after just three games to take the reins at Notts County, before managing the Bees for a third time for the final three games of last season, although he was not kept on over the summer and was duly appointed in charge of the Gills.
Barnet could hand a debut to David Stephens. The defender arrived on transfer deadline day last week from Hibernian but was not signed in time to face Rochdale on Saturday.
Striker Jon Nurse and goalkeeper Liam O'Brien will be checked over ahead of the clash.
Nurse missed the 2-0 defeat at Spotland after being diagnosed with concussion at York the week before and O'Brien was absent due to a groin problem sustained in training meaning former Arsenal keeper Graham Stack made his Bees debut.
Defender Danny Senda and striker Steve Kabba remain on the sidelines as they continue to recover from long-term knee injuries suffered last season.