Acher Kain Versus Acher Kach

Question

It seems there are two Versions of Al Hanissim one says Kain one says Kach which one is right and what is the underlying logic for each?

Answer 1

ואחר כן is the Biblical Hebrew form (e.g., Lev. 14:36), while ואחר כך is Rabbinical Hebrew (e.g., Berachos 2:2). So this is one instance of the more general debate as to whether the prayers should follow Biblical Hebrew precedents where possible, or whether this isn't important.

In this case, the older version was ואחר כך; R' Shabse Sofer, a prominent grammarian of the 17th century (whose siddur was indeed considered to be a model of proper dikduk) suggested saying ואחר כן instead, and so this became a popular variant.