Hi Vasanth,
If the budgies are related, you should not try to hatch the eggs. When you let related birds breed, the offspring often do not survive and if they do, they can have deformities or internal problems or genetic weaknesses that causes the bird to have health problems and a short life span. A budgie egg would have to be incubated in a commercial incubator that has humidity control and a thermostat to maintain the right temperature. The eggs also have to be turned regularly. Then if the chicks hatch, they have to be fed hourly around the clock and kept in a brooder. Even then, budgie chicks that are hand fed from day one rarely survive. It is a lot of expense to end up with a dead chick.
When you breed budgies or any bird, you should only have one pair of birds in each cage. And when the chicks are weaned, they need to be separated from the adults so that they do not breed when they are old enough. You should not keep the male and female chicks together or they will breed and again, you should never allow this. Budgies should not be paired to breed until the male is at least one year old and the female 18 months to 2 years old. They would never breed at such a young age in the wild, but in captivity they tend to mature when they are still too young to know what to do.
I would separate the young bird from any adults and not let it breed until it is old enough. And again, you should not breed it with its parents or brothers or sisters.
Thank you for asking Lafeber,
Brenda