hi there,
I got a part time job offer and I was told that I will be issued Form 1099 at the end of year for the remuneration I will receive for the part time job. I am on h1b visa and in the process of getting my green card in next few months. Is it legal for me to submit Form 1099 along with my W2 issued by my H1B holder?
Thanks!

Your H1B visa only permits you to work for the employer who sponsored it.
You cannot legally work for any other company except that one while you are on an H1B visa as I understand it.