H1b Stamping

I have a valid stamped visa (H1b) till 20th Aug 2016 in my passport and I am currently in India and recently got my extension approved and an approval notice I-797A came in which it is shown as valid from date as 21st Aug 2016. In this scenario is that I can travel back to USA with my existing stamped visa in passport and after 8/20 the newly approved I-797A will come into effect ?

At present my family is USA and I came to India after my existing extension is filed and after coming here I have it approved and I-797A approval notice came.

Can you please let me know if there will be any problem ? or any suggestions on how to take the above situation.

My motive is return back to USA as soon as possible and re-unite with my family

You can return to US using current petition and visa stamp. When entering US, show your new petition to PoE officer and he should issue I-94 based on new 797. This would allow you to stay and work until extended 797. If PoE issues I-94 based on old (current) 797, then that would expire on 8/20.