What is the ruling on money brought by a crow each time, its source unknown, and how should this crow be dealt with?

You have no right to this money. It is akin to lost funds that are spent on the poor or for the benefit of Muslims if their owners cannot be found. Al-Shabramallisi mentioned in his commentary that items found in a crow's nest or similar places could either be a lost item that needs to be announced, or it could be like something blown into a house by the wind and is not considered a lost item, in which case it belongs to the public treasury (Bayt al-Mal). You must prevent the crow from taking people's money, even if it means confining it or removing it from your possession.