This can best be achieved by DNA analysis of the three individuals.
The DNA of an individual is almost exactly the same in each and every cell of that individual. This genetic material is determined from the genetic material of both his father and mother. Sexual reproduction involves shuffling the DNA of both the father and the mother and then bringing them together in a cell that has its own unique combination of genetic material. The genetic material of an individual is derived from the genetic material of the parents of that individual. This genetic material is known as the nuclear genome of the individual, because it is found in the nucleus.
Comparing the DNA sequence of an individual to that of another individual can show if one of them was derived from the other or not. Specfic sequences are usually looked at to see if they were copied verbatim from one of the individuals genome to the other. If that was the case, then this proves that the genetic material of one individual was derived from that of the other (i.e.: one is the parent of the other). This way, paternity can be proved or disproved.
Besides the nuclear DNA in the nucleus, the mitochondria in the cells also have their own genetic material termed the mitochondrial genome. There is much less mitochondrial DNA than chromosomal DNA, and mitochondrial DNA comes only from the mother, without any shuffling.
Proving a relationship based on comparison of the mitochondrial genome is much easier than that based on the nuclear genome. However, testing the mitochondrial genome can only prove if two individuals are related by common descent through maternal lines only from a common ancestor.