There is no widely known figure or historical person named Lyncoca. It is possible that this is a misspelling or a less popular/personal name associated with someone or something not widely recognized.
Andrew Jackson did not kill his adopted son, Lyncoca. Lyncoca died of disease.
Yes he did after he killed the child's parents. The Indian child's name was Lyncoca. He adopted him in 1813 after a battle . This child had died several years later due to a contraction of a European-based disease.