you can make application for child custody in India 

2) welfare of child is paramount consideration 

Decision as to right  of child custody depends on many factors like age of child, state of residence of child in U.S. earning capacity of parents seeking custody etc. Even after expiry of visa child is not necessarily deported ignoring the possession of child by mother. Without details it is not possible to give actionable advice.

You obtain an order for child custody in your favor from the USA court and then file an execution petition before the concerned court in India to execute the child custody orders. 

you have to file  execution petition in family court in India in city where child is residing 

Dear Client,

If your wife has taken your U.S.-born child to India without your consent, enforcing U.S. court orders for the child's return can be challenging, especially since India is not a signatory to the Hague Convention on International Child Abduction. However, you can seek enforcement of the U.S. custody order by filing a petition in an Indian court under Section 13 of the Code of Civil Procedure, 1908, which deals with the recognition of foreign judgments. You may file this petition in the High Court or Family Court where your wife and child currently reside in India. While the Indian court will focus on the child's best interests, presenting a certified copy of the U.S. court order and demonstrating that returning to the U.S. aligns with those interests could support your case. Despite potential challenges, such as jurisdictional issues and the Indian court's discretion, a well-argued petition could lead to the enforcement of your custody rights.

US court order regarding child custody wont be enforce in India. You have to apply for custody in lower court where child is residing. 

If the child is taken without your consent from USA  then filing a habeaus corpus would be  very efficacious remedy.

You will have to file such writ petition in the high court of the state where the child is presently kept.

Contact an advocate to get better idea for such legal remedy. 

- If that said custody order was passed by the US Court in the presence of your wife i.e. she has participated in the proceeding of the case in US , then that order is valid in India. 

- You can file an Execution petition in family Court in India to get the custody of the kid 

- Further, if she has taken that kid to India without taking your consent and knowledge then you can file a complaint in US police for kidnapping and submit that copy of the complaint before the Indian Court with the execution petition. 

If you are able to obtain a child custody decree in your favor, considering the child's welfare as paramount as well as since the child is an US citizen, the execution petition filed before the family court or the district court within the jurisdiction where your wife currently resides in India will be the best option before you to get back the child custody through legal process. 

In your case, you must file a petition of for permanent custody in the courts of USA, followed by an application for interim visitation rights. You can file that in Indian courts as well. The court will be family court (within a district court).