No difference. I'd guess "in" is more common.

I would use 'with.' We would say shiver with cold/fear/delight. For example:"She was shivering with cold as she played in the snow." Shiver normally used because you are cold or frightened. It suggests a slight shaking movement of your body caused by cold or fear. Similarly, you could say 'tremble' with fear.'

In my opinion, both are correct but differ a little in connotation. He shivered in fear. = He shivered in the face of fear. (?) He shivered with fear. = He shivered because he was afraid. It is a good question and I don't know if "shiver in fear" is standard American English, but do know that "shiver with fear" is a standard idiom. I'll mull this over and let you know if I change my mind about my response to your question. Edited to add: "Shiver in fear of ~" Perhaps you saw "shiver in fear of (something)". This is a common expression. He shivered in fear of death.

Hello, dolco! You can use "shiver in" when you talk about the cold environment. And "shiver with" when you talk about fear. So the answer is shiver with fear.