The correct answer is option 'A', Hominids.

Explanation:

Genus is a taxonomic rank used in the classification of organisms. It is a category that groups together closely related species. In the context of the question, the genus referred to is related to human evolution and the classification of human ancestors.

- Hominids:
The branch of Genus that is relevant to the question is Hominids. Hominids are a group of primates that includes modern humans (Homo sapiens) and their closest relatives, both living and extinct. This group also includes some extinct species such as Neanderthals and Denisovans. Hominids are characterized by their bipedalism, large brain size, and complex social behaviors.

- Hominoids:
Hominoids are a larger taxonomic group that includes both living and extinct apes and humans. This group includes the family Hominidae, which consists of orangutans, gorillas, chimpanzees, bonobos, and humans. Hominoids are characterized by their larger body size, lack of a tail, and more complex behavior compared to other primates.

- Neanderthalensis:
Neanderthalensis refers to the species Neanderthals, which is an extinct member of the genus Homo. Neanderthals are closely related to modern humans and share a common ancestor. They lived in Europe and parts of Asia from about 400,000 to 40,000 years ago. While they are part of the broader hominid group, they do not represent the entire branch of Genus.

- Australopithecus:
Australopithecus is another genus within the hominid branch. It includes several extinct species that lived in Africa between 4.2 and 1.2 million years ago. Australopithecus species are considered to be early human ancestors and are known for their bipedal locomotion. They are believed to have been more closely related to the genus Homo than to other living hominoids.

In conclusion, the branch of Genus referred to in the question is Hominids, which includes modern humans and their closest relatives. Hominids are characterized by their bipedalism, large brain size, and complex social behaviors. The other options mentioned (Hominoids, Neanderthalensis, and Australopithecus) are also relevant to human evolution but do not encompass the entire branch of Genus.