Company wants to frame me for Dual Employment

Hello sir, I am working full time in X company, were in the appointment letter it was mentioned that I couldn't join any other company while working here. I joined on "September 1, 2020". We also have a family business (Y company) doing the some of the same services as my present employer but started long back in 2014. I was just a mentor there occasionally helping their team as it has a completely separate setup. I have never taken any salary, there were no formal appointments, no PF nothing. The proprietorship is with my MOM's name. Now the new management of X company, because of some relocation issues, wants to use this pointer, as they saw in my LinkedIn I have mentioned myself as co-founder of the Y company and constantly threatening me to take legal actions against me. They also mentioned that I am still an employee of X company, but already collected my laptop, access card everything, but now denying that I volenterally submitted them to X company. Now in this complex situation, I want to seek your help, to understand whether they can really take any legal steps against me.