Theory:

Evidences from Embryology:
The study involving the process of development of an organism from an embryo and the related  aspects is embryology.
During the early stages of development, the embryos from fish to mammals show huge similarities. However, the differentiation of their special characters appears in the later stages of development.
 
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Embryological evidences between different organisms embryos
 
The similarities in the early embryonic stages of the organisms show the common ancestry of these organisms.
 
These evidences were disapproved by Karl Ernst von Baer as he noticed that embryos never pass through the adult stages of other animals.
 
Biogenetic law or Recapitulation theory:
  
It is a theory given by Ernst Haeckel. According to this theory, ontogeny recapitulates Phylogeny, which means the stages of development of the individual animal repeats the evolutionary history of the entire race of the animal.
Ontogeny is the process of an organism's development from the zygote stage to adulthood, which encompasses the full lifespan of the organism. The development of a group of creatures from another group throughout evolution is referred to as phylogeny. Phylogeny essentially explains how different types of organisms are related to one another. A set of organisms' morphological and anatomical traits, as well as metabolism, change throughout time as they evolve. These changes result in the emergence of new species. Throughout their lives, new species' creatures go through the process of development. This is how ontogeny and phylogeny repeat themselves, forming the foundation for evolutionary hierarchy.
Molecular phylogeny:
  
According to molecular phylogeny, distantly related organisms accrue more differences in their DNA. The study of these differences aids in the deciphering of evolutionary links between organisms. This molecular phylogeny-based interaction between organisms corresponds to modern classification schemes.
Evidences from palaeontology:
The study of the history of life, which deals fossils, is known as palaeontology. Leonardo da Vinci is known as the father of Palaeontology. The study of fossils aids our understanding of the evolutionary history of numerous invertebrates and vertebrates. From simple to sophisticated species, evolution has undergone a lengthy process, according to fossil records.

The palaeontological evidence supports the genesis of contemporary birds.
  
Archaeopteryx:
 
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Archeopteryx
  
It is the oldest fossil bird. It was a Jurassic period form that looked like a bird. It was thought to serve as a link between reptiles and birds. It had feathered wings, like a bird. Like a reptile, it featured a long tail, clawed digits, and conical teeth.
Connecting links:
  
The properties of two different groups of live plants or animals have been discovered in some creatures. Animals like these are known as connecting links. The earlier group of creatures is thought to have given rise to the latter group of species. Some species can be found in the space between these two classes. These species exhibit traits from both groups.
Reference:
https://commons.wikimedia.org/wiki/File:Archaeopteryx_fossil.jpg