As far as taxation of your salary in India is concerned , it will be taxable in India since you will be receiving Salary in India from an Indian Company for your services in India . In that case , it is immaterial if you are resident or Non Resident.
As per Double Taxation Avoidance Agreement signed between India and USA , you being USA citizen ,may get deduction in USA from taxation as per Article 25 of the DTAA which is given below:
Article 25 - Relief from double taxation – 1. In accordance with the provisions and subject to the limitations of the law of the United States (as it may be amended from time to time without changing the general principle hereof), the United States shall allow to a resident or citizen of the United States as a credit against the United States tax on income
(a) the income-tax paid to India by or on behalf of such citizen or resident“.
Regarding USA taxation, of which I am not expert , ask somebody there.
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