A: Missing from your question is *why* you think you were treated differently. If you were not considered for the position because of race, gender, age, disability, or some other protected class or protected conduct, then you may have a claim worth pursuing.
A: Minnesota is an "at will" employment state so generally speaking you can be fired for just about any reason, so long as it is not discriminatory or retaliatory. The law does not require people to treat you nicely. But if you can show that you were terminated because of your race, gender, disability, age, etc., then you may have a case. You should discuss the specifics of your situation with an employment attorney to see if there is anything.