Can I be sued for contracts and payments that had nothing to do with a new employer?

I currently own and run my own LLC Business. Recently I started working for another company. While working for them I still continued to run my own company. I had open contracts that I had signed prior to signing on with them. The clients I had paid me directly for my work. However the company I was working for feels they should be paid the money and give me a 8% share of it. Can they do this? I no longer work for them. They still have me listed as an expert on their website and they still have work they have not paid me for. I have requested payment numerous times. What can I do? They've threaten to sue me.