It will be a problem for your child to travel to India and return to the US.
According to US law, anyone born in the US is a US citizen, and as such requires a US passport to enter the US by air.
Meanwhile, if Indian immigration sees he has no US visa and stamps in his Indian passport (and he cannot get a US visa as a US citizen), they will know he has another nationality too, with the following consequences.
So there are only two ways for your kid to travel to India and back to the US while you still live in the US:
(recommended): Get your baby a US passport and overseas citizenship of India (OCI). It’s allowed to have both OCI and US citizenship, and OCI allows you to live in India permanently, but not vote or hold government positions. Furthermore, it is easy for an OCI holder to get Indian citizenship back.
Get your baby an Indian passport, travel to and from the US through the Canadian or Mexican land border, and fly to/from Canada/Mexico. At the US land border, your child’s US birth certificate can be used to enter the US.
This way, you have to get a Canadian/Mexican double-entry transit visa in order to enter Canada/Mexico.
Credit:stackoverflow.com‘