Comparative DNA analysis is a very popular procedure to include or exclude individuals from consideration as suspects at a crime scene.
However, since every person’s mitochondrial DNA is of maternal origin, it is also easy with mitochondrial DNA to prove that all children borne of a certain mother, both the males and the females, are hers. That is because the mitochondria are only found in the cytoplasm and the sperm which fertilizes an oocyte (egg cell) does not have any cytoplasm. At least that is the theory.
It would be easy to prove this with cellular autoradiography using tritiated thymidine, providing such experiments met the medical code of ethics (probably not) and only if our cousins – the chimpanzes – wouldn’t mind.