Your question is bit confusing, but if I understand correctly you are asking how to claim GST ITC in Karnataka and Tamil Nadu when you are originally from Gujarat.

1. When you transfer your products from GUJ to KA or TN, you issue a Stock transfer invoice. The IGST show in this ST invoice is your Output GST in GUJ. When the product reaches KA , same IGST is input in your KA GST No.

2. So when you make sales in KA, input is the ST invoice GST and output is as per your sales.

3. So, wherever you are purchasing, that GST state gets the input, ST shows the output. The recipient state shows as input and your sales gives you the output.