'Scream in fear' is more common and sounds more natural. 'Scream with fear' isn't wrong though. It would be understood. If you look at the Google ngrams result, you can see that 'scream in fear' is far common

Both “screamed in fear” and “screamed with fear” are grammatically correct, however they do have a subtle difference in their nuance. While “screamed in fear” emphasizes the *internal emotional state* that caused the scream and suggests that fear is the reason/cause of the scream, “screamed with fear” suggests that the person/people screamed and that fear was accompanying the scream. Screamed in fear is used much more frequently both in literature and in everyday language, however, “screamed with fear” can, for example, be used for stylistic variation in writing.

You can also use "from" and "out of". ChatGPT gave me 18 prepositions that work to varying degrees, emphasizing different things. Just go to an AI engine and type: "Give me as many prepositions as you can to fill in the blank: 'She screamed ____ fear'." Also, explain the nuances.

thank you so much for quick response.