How do you tell someone to stop interrupting your conversations with other people?

Answer 1

go up to them and tell them to say it to your face. if they have to say it to your face they most likley will stop talking. or whatever they are saying just know thats just what they think not the truth.

Answer 2

You say to them in private when no one else is listening:

You're my friend, and I value what you are saying, but please wait until I have finished my conversation with this other person before you start another one while I am still talking.

If they don't understand that, then try it a different way, you say:

Wait for me to finish talking before you say something.