In which month of the pregnancy we can perform the DNA test of the coming baby

After the baby is born,

Unless there is serious health issues or other medical issues, it will not be done before birth due to the danger to the child.

What DNA test? If you are referring to a test to determine paternity, no doctor is going to perform one because of the health risks.

Note: I was annoyed when Sunday night's episode of ABC's Revenge showed a paternity test being done on a still pregnant character.

The procedure is called an amniocentesis and it is usually only done for diagnostic purposes if there is a problem with the mother or fetus.

Due to the risks to both mother and baby a doctor will not perform an amnio strictly for paternity reasons. You will have to wait until the child is born for a DNA test to be done.