Perhaps you mean genetics. Genetics is a branch of Biology that studies the inheritance of the characters. Her relevance has gone growing with the time because the role of DNA and genes in determining the structure and functions of an human being (and not only humans: animals, plants and even bacteria and viruses) and its defects. Today we know that almost the totality of human diseases, except for the traumatic ones, have a genetic component, from stroke to cancer.
The genitive case is the possessive case. In English. there is not an actual grammatical case for genitive; there are the possessive 's, the possessive of.
For example, "What is your dad's name?" is a question using the possessive, or genitive: dad's
The genitive, or possessive, is also used as a partitive in English, using the word of, for example, a piece of bread.
Many languages have an actual genitive case. In such languages, there are generally different word endings which show the relationships between the words.