Words derived from Latin series appear only from the eighteenth century in both English and French. This isolated Anglo-Norman use may therefore be suspect, despite having a parallel in medieval Latin serialiter.
adv.
1in order, one after the other:
(
c.1270; MS: s.xiii4/4
)
Fet en cest livere cunter e dire Des miracles seint Richard seriaument
M49
seriaument (c.1270)