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Characters from someone else's story are typically protected under copyright law, especially if they are well-defined and original. Using such characters without permission can constitute copyright infringement. This is true regardless of whether the characters appear briefly or play a significant role in your story.
Non-commercial, transformative uses (like parody, commentary, or critique) are more likely to be fair use.
Using factual or historical elements is more permissible than using fictional elements.
Using only small portions of the original work may weigh in favor of fair use.
If your use does not harm the market for the original work, it may support fair use.
Some characters, especially famous ones, may also be protected under trademark law. If your use of the character creates confusion or implies endorsement by the rights holder, it may violate trademark law.
Fan fiction often involves the use of copyrighted characters. While many creators tolerate non-commercial fan fiction, it is still technically a copyright infringement unless explicitly allowed. Some creators enforce their rights more strictly than others.
If using existing characters, make the use as transformative as possible, such as in parody or critique.