How to deal with bossy coworkers who think they can set my priorities?

I work for several customer groups and one of them (the least important in the company) is formed by a bunch of egomaniacs who think they’re the boss of everyone else.
When they have a request, they will set up a meeting instead of filling up the story or an equivalent form. Then they expect me to deliver their projects “as soon as possible”; while continuously ignoring my requests for inputs or clarification. This has been the case for almost …

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