"Satisfied with" vs. "satisfied by" vs. "satisfied in"

"He was satisfied with his test results" means that he was happy with them. The test results meet his expectations (dictionary.com, definition 1).

"He was satisfied by his test results" is similar, but has the idea that the first he had some need or other metaphorical container filled by the test results of the second he (the two references to he may refer to the same person or to different people). For example, a teacher (the first he) who had spent a lot of personal time with a student (the second he) might consider the favour repaid (i.e. satisfied by) the student's good results. Depending on context, it could also have other shades of meaning - see the dictionary.com entries after #1.

"Satisfied in" is not a grammatical construction.

Here's another example. If Sam is fed some food that fills him up but which isn't really very good quality, you might say that Sam (or more precisely, Sam's hunger) is satisfied by the food, and that Sam is not satisfied with the food.

He was satisfied with his test result.

This one is idiomatic, meaning the person was pleased or happy with the result. Satisfied is an adjective here, and it collocates with the preposition "with":

satisfied (adjective): pleased with what has happened or with what you have achieved
satisfied with: The President declared himself satisfied with the progress of the talks.

(Macmillan Dictionary)

He was satisfied by his test result.

It's not ungrammatical, but it sounds a bit awkward. Satisfied is a verb (passive voice) here, and the sentence is grammatically equivalent to The test result satisfied him (active voice).

He was satisfied in his test result.

This does not sound idiomatic or grammatical to me.