In some fanfictions, it could be a more emotional moment. Sirius has a deep connection with Harry, and perhaps he pins Harry down in a moment of intense fear or worry. Like if Harry was about to sacrifice himself for something, and Sirius couldn't bear the thought of losing him, so he physically restrains him.
It might also be a situation where Sirius is frustrated with Harry for doing something reckless. He pins Harry down to get him to listen and understand the seriousness of his actions. For example, if Harry was planning to go after a powerful enemy alone without a proper plan.