Can a pediatrician work 3 times a week?

Pediatricians see patients for well visits and sick visits at least five days a week. Then they are on call for emergencies overnight and on the weekends. That's why they work in a partnership with other pediatricians, so they can share the load and cover for each other.

As a parent, even if I liked a particular pediatrician, if that doctor's office is only open three days a week, I'm going to find a different practice.

You could have office hours 3 or 4 times a week but you would still be required to answer parents phone call and often go to the hospital on the other days.

Ideally a doctor like this would find a partner to cover the other days so the acutely ill patients would always have access to one of them. I do know a dentist who has a similar arrangement where each works full time for part of the year while the other one takes extended vacations.