Unkind children causing bickering to happen

I am not sure if my initial message went through. I am having trouble with my three children ages 98 and six constantly being unkind to each other and saying mean things to one another and putting each other down. For example this morning my daughter said to my son “well that’s because you don’t know how to do anything and you can’t get it done. Your not smart” these negative comments and quips are causing them to fight constantly and it has created a lot of negative energy around the house. I have recently started telling them that if they are unkind and say mean things to one another that is a “no answer and they will earn an extra chore. I’m not sure if this is the correct approach or what else I can be doing. Thank you for your input here.
God bless you and your work,