At what age do children with depression and schizophrenia generally begin to think about suicide if ever?

Varies: Children and adolescents can attempt suicide at any age but the most common is in pre-adolescence and adolescence. Younger children will often exclaim they wish they were dead, but this is rarely a cause for alarm, it usually uttered in anger and frustration. Any credible suicide threat should be considered an urgent problem, and you should consult your doctor immediately..

Almost Anytime: Children with serious psychiatric problems can have suicidal thoughts at almost any age, although it is very rare in preschool children and uncommon in elementary school age children. Also, you mention schizophrenia in your question. I would want to mention that schizophrenia is rare at ages younger than late adolescence.

Any age: Depression and suicidality is not age dependent but can vary for every individual

At any point: This could occur at any point. Has your child been diagnosed with schizophrenia and depression? Definitely see a board certified pediatric psychiatrist for diagnosis and treatment. Frequent counseling will also be part of the treatment plan. His visits both medical and counseling will screen for any suicidal tendencies. Best of luck!

SUICIDAL THOUGHTS: Children can have suicidal thoughts at any age. Young children and youths with severe mental illness don't understand the finality of death & may want to be reunited with a grandparent. Please take your child to a Clinical Psychologist with expertise in multiple types of psychotherapy & a Psychiatrist to discuss medication, & a Physician for a physical exam to rule out illness.