Order received from Overseas company to deliver material within India

As per the definition of export  of goods ,  given in section 2(5) of the IGST Act 2017 (please refer) , registerd person has to take goods outside India to the place out side India, in your case goods are not delivered outside India, therefore this is not a case of export of goods , this is the case of  Bill to Ship to  10(1) b of the IGST act ,therefore  you have to charge IGST  to your claint , as you are billing to USA Claint  and shiping   in India . 

You may requried  to take FIRC ( Foreign  Inward remitance  certificate )  form BANk , however this certificate is required in case export of Goods or services . 

Take more opinion on this from others also.

I  have corrected  my earlier reply above please refer , you have to charge  IGST and not CGST/SGST . 

Means 1st buyer is out of state so it will attract IGST instead of CGST/SGST, though material movement is within same state.

Yes , You are biilling  to US Client  therefore  IGST  , and shiping  in  india  . ( Bill to ship to case )

 not export  case  . also take more Opnion on  this . 

One thing is clear... it will be not be cconsidered as an Export of Supplies.

I am assuming that the goods that you wish to supply in India is a DTA market. If it were in a SEZ, then you would need to obtain the relevant Bill of Export and submit it to the bank in order to set off the EDPMS obligation.

For supplies in DTA, there is no such document that would consider valid. Hence, inform your bank in advance and check with the prospects of settling the transaction. When the payment is effected by the U.S. based Company, MT103 (SWIFT) must show the "Purpose Code" which is other than exports and in close relevance of the supplies made in India.