Role of の and meaning in the sentence "その瞬間の自分の手に〇〇がにぎられている"

Question

The complete sentence, although I don't think it is necessary, is the following:

その瞬間の自分の手に、人類すべての運命を決定付けるような、重大なターニングポイントがにぎられているなんていうことは、分かるはずがないんた

So, if the intended role of その瞬間 was to be "in that moment" wouldn't it be その瞬間に instead of の? Or is it that 瞬間 acts like an adverb or "の adjective" here and transforms the meaning of the sentence into something like "I was holding such and such for such a short moment".

I don't really know if my possible interpretations make any sense, so I hope I can get some help.

Answer 1

The の is normal of.

You can use に as well.

1. その瞬間の自分の手にXがにぎられている
2. その瞬間に自分の手にXがにぎられている

are both fine, literally corresponding to

1. X is held by my hand of that moment.
2. X is held by my hand in that moment.

'My hand' in a particular moment can be called 'my hand of that moment' (in Japanese, at least).

Answer 2

I showed the difference in nuances bellow.

その瞬間に自分の手にXが握られている: X would being held by my hand that time.

その瞬間の自分の手にXが握られている: X is held by my that-timed hand.

From the former, I feel a little strange sensation. Because of the repetition of ”に” (その瞬間に自分の手に). So the latter is more appropriate and cool expression!!.