I want to ask we have a parrot in our house but people says not to keep it. It may curse you to keep him in a cage and therefore free him.
But my father gave them excuse that Imam Ali a.s also had swan who stopped him on 19 Mahe Ramazan so it should be fine.

Can you please guide me with a hadith if possible ruling of Maraje on this

There is no problem in keeping it.