Can he get custody of my kids if I have depression/bipolar but hes a felon?

I have soul custody, legal and physical of our two kids, he wants to say Im unfit and mentally unstable, and he needs soul custody, but hes a felon who does not see his pro.officer, has several warrants a child by a 15 yr old (now 20, hes 35) and is a true alcoholic. While i am clean from the law and take depression meds, but still have a job own a house and vehicle with my first borns dad to back up I am a great mom. Is there a chance he could win??