First you need to file for child custody under Hindu Minority & Guardianship Act, 1956 (Applicable if you are hindu) OR Guardian & Wards Act, 1890(Applicable for other religions).
The supreme court in the case of ROXANN SHARMA V/S ARUN SHARMA, CIVIL APPEAL No. 1966 OF 2015, has stated that a father can be guardian of the property of the minor child but not the guardian of his person if the child is less than five years old.
The court also made the following comments: "The Court said that there can be no cavil that when a Court is confronted by conflicting claims of custody there are no rights of the parents which have to be enforced; the child is not a chattel or a ball that is bounced to and fro the parents. It is only the child's welfare which is the focal point for consideration. Parliament rightly thinks that the custody of a child less than five years of age should ordinarily be with the mother and this expectation can be deviated from only for strong reasons."
Coming to your other questions:
1) Estimates on court fee: Court fee costs Rs10-/-. Lawyer fees depends on his standing in his profession.
2) What can be adverse legal things to this action of mine in court from my wife side in court ?
Normally once you file a child custody petition, there will be counter cases filed against you by your wife under Domestic violence and Dowry cases. No worries as the courts now have issued guidelines to police and courts to resolve as much as possible through counselling and only if the conduct of the party warrants an arrest, should be arrested after following the guidelines.
3. What is probability of success outcome of this thing ?
We have stated the position of law. However , success outcome depends on many factors including your ability to earn and support the children's education, medical and other financial needs, mental and moral support that you can give the children etc. In case your wife is also contesting the custody with ferocity, the courts may ask the children their opinion too and shall decide the case only on what is best for children. The courts when granting custody will only look at the best interests of the children.