Pediatrics (or pediatric medicine) was the branch of medical science that specialized in the care of infants, children, and adolescents.
Doctor Julian Bashir graduated first in his class at Starfleet Academy in pediatric medicine in 2368. In 2372, he mentioned this during a discussion between Miles O'Brien and his fellow crewmates. In this discussion, he explained that his daughter Molly had been crawling into bed with him and his wife, who was pregnant, for the past two months. Jadzia Dax, recalled that when she was Lela Dax, her son Ahjess would do the same thing, and explained that Molly "just needs a little attention." Bashir agreed with Dax, and further explained that he would even say that Molly was jealous, because she knew that Miles and Keiko were going to have a baby soon. (DS9: "To the Death")
In 2372, Kes sought The Doctor's guidance while she was going through the Ocampan process of elogium. While The Doctor acknowledged he was programmed to discuss delivery methods and pediatric situations, he felt unable to offer much of a perspective on becoming a parent. (VOY: "Elogium")
When The Doctor created his own holographic family in 2373, which B'Elanna Torres later "tweaked" to make more "real", he remained confident that he would be able to adapt to her modifications. The Doctor felt that due to the fact that his database "contains everything there is to know about pediatric care and childhood development," he could not imagine a parenting problem that he could not handle. (VOY: "Real Life")
In 2377, when The Doctor began to take care of the pregnant B'Elanna Torres, he proceeded to expand his medical database in obstetrics and pediatrics. As a result, he put together a prenatal enrichment program for Torres, which he eventually expanded into a parenting class for both her and her husband, Tom Paris. (VOY: "Lineage")