Cotton Oneil Clinic. Nursing (Nurse Practitioner), Internal Medicine • 25 Providers. 901 SW Garfield Ave, Topeka KS, 66606. Make an Appointment. (785) 354-9591. Telehealth services available. Cotton Oneil Clinic is a medical group practice located in Topeka, KS that specializes in Nursing (Nurse Practitioner) and Internal Medicine..