I am currently living in USA and my h1b petition picked up in lottery. But my passport will be expiring in Jan 2021. will it affect the validity of my H1b approval?
No, it will not affect it. Use your old passport and apply for the H1B.
You can get new passport after your H1B process is complete. Your New passport will have old passport number, so you will be fine.
Thanks Kumar. Hope my new i94 (h1b) is not based on my current passport which is expiring 01/21.
It will very likely be given until end of your passport. You will need to apply for new passport after approval and get I-94 corrected. read below