I'm not so sure that the first sentence is grammatically correct so let's try breaking down the second sentence:
This indicates that a context has been established (or will be established) - i.e out of 3 weird cases, the second case is the weirdest and by establishing context you are making it very specific (non-generic) - not any other case but this particular case: the 2nd case out of the 3 weird cases.
This is the weirdest...
When using superlatives, you normally use an indefinite article (the) because using a definite article (a) wouldn't make sense, i.e you wouldn't say "This is a weirdest...". You can take a look at this answer for more clarification.
This is the weirdest case of a scientific field.
Now we start to deal with countable vs uncountable nouns. Scientific field is a countable noun (i.e you can count how many fields there are: Physics, Chemistry, Biology, etc) - I'm grouping the word "scientific" with the word "field" but the important part here is "field" because we have many scientific fields and using a means you are picking a particular field (out of the many fields we have).
Summary - go with the 2nd sentence, because it would mean:
Out of the many scientific fields we have, we'll be focusing on a
particular field: Physics. And, out of the 3 weird cases we have
established (or will establish), case #2 is the weirdest.
But with most things in English, you will find exceptions.