Background Mental health issues in children and adolescents are quite significant. Despite their impact, research on psychiatric disorders in these age groups is limited. This study aims to evaluate the prescription patterns of psychiatric medications and the prevalence of psychiatric disorders among children and adolescent age group patients. Purpose This study aims to evaluate the prescription pattern of psychiatric medications and the pattern of psychiatric illnesses among child and adolescent age group patients at a tertiary care hospital in India. Methods This hospital-based observational study was conducted over 1.5 years at the Government Hospital for Mental Care in Visakhapatnam, India. A total of 150 patients aged 2–18 years, diagnosed with psychiatric disorders and prescribed at least one psychiatric drug, were included. Data on patient demographics, diagnoses, and prescription details were collected and analyzed using SPSS version 2022, following WHO drug use indicators. Cost analysis compared drug costs within the hospital pharmacy and external pharmacies. Results The study population comprised 56% children (2–10 years) and 44% adolescents (11–18 years), with a male predominance in both groups. The average number of medications per prescription was 2–4, with 94% prescribed by generic names and no use of fixed drug combinations or injectable drugs. Mental retardation was the most common disorder, followed by attention deficit hyperactive disorder (ADHD) in children and oppositional defiant disorder (ODD), bipolar disorder, and schizophrenia in adolescents. Risperidone, trihexyphenidyl, carbamazepine, and valproate were the most commonly prescribed medications. Most drugs were available at the hospital pharmacy, minimizing the financial burden on patients. Cost analysis showed significant variations in drug prices outside the hospital. Conclusion The study highlights the rational prescription trends among child and adolescent psychiatric patients. There was preference for atypical antipsychotics and newer drug classes over conventional medications. Polypharmacy was up to the mark. The findings emphasize the need for periodic prescription monitoring to ensure safe, effective, and cost-efficient treatment.