Meaning of 所 in "有所..." As far as I know, 所 has the following meanings:

a place, as in 派出所 (police office).
a counter, as in 一所科學中心 (a science center).
a passive voice indicator that pairs up with 被（為）, as in 被（為）愛所糾纏 (tangled by love).
a conjunction, as in 所熟悉的環境 (environment that I am familiar with).

EDIT: as Master Sparkles mentioned in the comments, 所 in the third and fourth context above also intensifies the association between the preceding noun and the verb that follows it.
However, in the following sentence,

希望我的回答能有所幫助（貢獻）。
Hopefully, my answer can be of some help/contribution.

none of the above meanings is appropriate. Besides, I thought that the sentence would be the same without 所, as in,

希望我的回答能有幫助（貢獻）。

As such, what is the meaning of 所 in the &quot;有所...&quot; construct? Or is it simply redundant?
Thanks in advance!
As you had said, 所 is not redundant. But to me, "有帮助" and "有所帮助" doesn't have that much differences, especially when you are in an oral conversation with Chinese people.

As for your explanation for "有所謂", the translation for "这件案子有所谓" is "This case matters." You are correct. But I don't think that it has the meaning of "has something that it says". Yes, "謂 = 說". However, the literal meaning of this is not strong when you say "有所谓". When hearing about "有所谓", please just take it as "matters", and just forget about its literal meaning.