If my ex is suffering from mental health problems can I apply for single custody or would supervised contacts be an option as I do want him to see our child

It's always helpful to let us know where you live because this is an international site and laws vary.

It is typically better for a child to have as much contact with both parents and the love and support of both parents as reasonably possible. If your ex's mental illness impacts his or her parenting capabilities, reliability, judgment or safety, supervised visitation is a good option.

You really need to talk with an attorney and find out what the courts in your jurisdiction generally do in similar situations, and what might be a reasonable accommodation that you can either get the other party to agree to, or win in court.

Of course, it's best for your child to have two parents, even if flawed. If the other parent is dangerous, unreliable or prone to act in frightening or inappropriate ways, visitation with supervision is probably reasonable. Some times there are conditions such as cooperating with mental health treatment - if the parent misses appointments or goes off meds, they cannot have their visitation. If illegal drugs are involved, passing a clean drug and alcohol screening can be set as a condition for parenting time. Many things are worked out for individual circumstances.

It's complex though so you will have to get an attorney in your area to help you with this one.

Did he have these problems when you made the child with him or is this something that recently happened? What type of mental health problems is it?