fight for something—
1. struggle to defend smth.:
- My Dad says we’ll all have to fight for our country when Der Tag comes. That’s German for the Day.
2. try in a determined way to get or achieve smth.:
- Having fought for the prize so long, Gordon is destined to find in it only disappointment.
fight over something—
1. struggle for the ownership of smth.:
- They were too apt to go to law and fight over their lands and fishing rights.
2. argue or struggle over an issue:
- The First World War was fought over a small thing. A mere scrap of paper.