Unless you are actually on the battlefield, "in" is not correct. It is better to say, "during". "At" is definitely wrong.

In world war II - correct In the second world war - correct At the second world war - not correct At world war II - not correct We never say 'at the second world war'. It's always 'in'. 'In' suggests that the war is going on around you. However, we could also say, 'At the time of the second world war' because the preposition refers to the time rather than to the war.

"In" is correct, and "at" is wrong, regardless of the convention you use for naming the war. Where did you get the idea from that the style of naming affected the preposition? The only time that 'at' can collocate with 'war' is in the adverbial phrase 'at war' - note the lack of article. For example, you might say "England was at war with France at that time".