The two sides also met in the North Yorkshire (North) area final last year, Sessay triumphing in a bowl-out after the elements had defeated both teams.
This season they will meet in the first round on Sunday April 30.
Staithes also lost out to Sessay in 2010 and 2014 so they will be wanting to buck this trend, Sessay winning by seven wickets in 2014 and by just five runs in their 2010 meeting.
Ebberston entertain Premier Division rivals Forge Valley in the same group, while Heslerton play host to Alne and Cayton are at home to Silton, with Flixton being handed a bye through to round two.
In the North Yorkshire (South) group, Staxton have been handed a bye through to round three on May 28.