Legally wedded wife has no right on child born out of husband with his mistress 

No. A legal wife does not automatically acquire any custody or visitation right over a child born to her husband and another woman merely because she is his legally wedded wife.
Assuming the parties are Hindu, the position would generally be:
The biological mother has the primary claim to custody, particularly when the child is very young. Under Section 6 of the Hindu Minority and Guardianship Act, the mother is ordinarily entitled to custody of a child below five years, subject always to the child's welfare. The Supreme Court has repeatedly held that the welfare of the child is paramount, rather than the competing legal rights of adults.The married man, if he is the biological father, may have guardianship/custody rights, but his pending divorce from his legal wife does not give that wife an independent parental status in relation to the child.
The legal wife would ordinarily be treated as a stepmother, not the child's legal mother. Section 6 of the Hindu Minority and Guardianship Act expressly distinguishes the natural parents from a stepmother/stepfather.
Therefore, the legal wife cannot ordinarily demand custody merely because she is married to the child's biological father. She would have to establish some independent basis showing that her involvement is in the child's welfare.
Visitation is somewhat different. A Family Court has broad jurisdiction to make arrangements concerning the child's welfare. In an appropriate case, a person who has a genuine relationship with the child may seek interaction/visitation, but a stepmother has no automatic statutory visitation right comparable to that of a biological parent. The ultimate test remains the child's welfare. The Supreme Court has emphasised that even parental rights yield to the welfare of the child.
What about the pending divorce?
The fact that the man's divorce case with his legal wife is pending does not improve her status vis-à-vis this child.
The divorce proceedings may, however, become relevant indirectly—for example, if the wife alleges that the husband is maintaining an extra-marital relationship, or if custody/maintenance issues arise in the matrimonial litigation.
If the husband has a child with another woman while his marriage is still subsisting, that can have matrimonial consequences in the divorce proceedings, but it does not thereby make his legal wife the child's parent.
If the legal wife wants custody
She would have to approach the appropriate Family Court/competent court under the applicable guardianship and custody law and establish why custody or interaction with her is necessary for the welfare of the child. Merely saying "I am the father's legally wedded wife" would ordinarily be insufficient.
Conversely, if the biological mother is providing proper care and there is no circumstance making her unfit, a claim by the legal wife for custody would ordinarily be difficult.
If you tell me (i) the child's age, (ii) whether the biological father has acknowledged paternity, (iii) whether the child is living with the biological mother or father, and (iv) whether the legal wife is seeking custody during the pending divorce or after divorce, I can explain the exact custody/visitation position and the possible remedy for each party

The man's legal wife is not the biological mother of that child who was born out of wedlock of the married man with another divorced woman. As such, the man's legal wife cannot legally claim custody or visiting right over that child in her divorce proceedings.

A DNA test will establish paternity beyond any doubt. The wife can request the court to subject her husband to a DNA test. Then, her allegation of adultery as a ground of divorce will only be strengthened.

Allegations of adultery  are proved of you establish husband is biological father of child 

take tjhe plea that husband is guilty of adultery and has filed false case 

judge can order a DNA test if paternity is directly in question and it serves the interest of justice.

The lady who is awaiting divorce from court cannot claim any rights over the child born to a different person even though it may be proved that the biological father of that child was her own spouse with whom the present divorce proceedings are pending before court.  She has no rights whatsoever over the child born to a different person for any reason.

The divorce case is already going on before the court of law. It will be decided on merits by the trial court. 

The acts of adultery or the child born to her husband out of anj extra marital relationship with another woman i.e., if the wife establishes via conclusive proof (such as DNA evidence or an admission of paternity) that her husband fathered a child with another woman while their marriage was legally subsisting then the decision of divorce may go in her favor. 

A judge will order a DNA test if it is indispensable to finding the truth in a dispute (such as proving or disproving an extramarital affair/adultery) and no other sufficient evidence exists.While a court can order a DNA test, it cannot physically force a person to give a sample. However, if the husband refuses to comply with a court-ordered DNA test, the court will draw an adverse inference against him under Indian evidence law (meaning the court will assume the test would have proven him to be the biological father).

Family courts strictly apply the rule that a person cannot take advantage of their own wrong. A husband who committed adultery and fathered a child outside marriage cannot claim that his wife subjected him to mental cruelty. The birth of the child automatically gives the wife a valid, legal justification to live separately. Thus, the husband's claim of "desertion" collapses.

The family court cannot force a divorce decree upon an unwilling, non-faulty wife simply by making the husband pay a large financial settlement.The court will dismiss the husband's petition outright. The husband remains legally married to his wife. 

The wife can either file a counter-petition for divorce on grounds of adultery and cruelty OR agree to convert the proceedings into a Mutual Consent Divorce.