Both my children get aggressive and fight with each other. Should I take sides with the one who is right, and reprimand the one who is wrong?

Unless you were witness to the conflict and saw how it started and who did what, you can’t be a judge of who is right and who is wrong. The right thing to do is to hold both responsible for the fight. At the same time, you should also hold each of them responsible at an individual level for having contributed to the conflict even if they think that the other one started it. This will teach them not to fuel conflict and to look for a reasonable solution on their own.