If your answer to a question is positive i.e. "Do you have any interns?" "Yes, I do have interns."
you can use 'do have' for emphasis. It's not necessary, but it stresses that you have interns or that your answer was positive.
You can also answer "Yes, I do." This is the short form so you don't have to repeat what was already in the question 'have interns'
You can answer "Yes, I have interns." This is the exact same as the first answer, but just isn't emphasized.