M.P.
You do not give us enough information to understand your situation and thus cannot answer your question in specifics. Who is supervising? Where will the visits take place?
I suggest that your attorney is the best one to answer this question. If you don't have one, you need one.
As to how do you do it, if you want to see your son (I hope you do) you just do it as ordered. Follow the rules and eventually, by showing that you co-operate you may be able to ask for the rules to be changed.
If you've been convicted of a crime then you may be stuck with this arrangement until your sentence is over. If you're wrongfully convicted, hire an attorney and appeal.
I looked at your previous posts and it seems that when you say convicted you're not referring to a crime but to the fact that CPS believed your ex's accusations. If this is the case, it's now a matter of showing that you are a good mother and one way to do that is to do all of those visits in a generous way. Yes, it's tough but the visits will get easier as you have more experience. Once CPS sees that you do co-operate with them and that you're appropriate during the visits the supervision requirement can be stopped.
You don't say what your ex's accusations are and so I can't respond to how to fight those accusations. If you don't have an attorney get one now.!
Who has custody of your son, now? Perhaps the father is also having supervised visits? If he has been given custody after 6 or so years of you having custody the situation must be quite serious. You need to find a way to show that your home, your parenting, and your ability to physically and emotionally care for him is greater than that of your ex. You may be able to consider this period of time as waiting for your ex to show that he's not as capable. If that happens then you need to have a history of co-operating with the authorities in order to regain custody.
Later: Could a part of the reason this is happening caused by your limiting his father's access to his son? I suggest that you consider the possibility of finding a way for you and your ex to work out a way to share your son. I urge you to continue with mediation and to focus less on his handicaps and more on how the two of you can work together to provide a more complete parenting plan for your son.