h1 b visa onsite oppurtunities

I had my h1 b visa stamping last month , valid for 2+ yrs. Am requesting my employer for onsite opportunities, but my employer says they donot have onsite oppurtunities now and offerring me offshore projects. Can i put down my papers and search for a new job. Does my employer have any right to cancel my visa, if i quit??

Employer can withdraw the petition. They can also cancel the visa stamp but for this they need to take custody of your passport and send it to consulate, which doesn’t happen often.

You can still approach another employer to file cap-exempt petition for you, even if the current petition has been withdrawn.