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I did my residency on H-1B visa. I think you are eligible to apply for this visa is you have passed steps 1,2, and 3. But I heard that lately some programs do not want to sponsor people on H-1B visa. It depends, you would have to see when you go for the interviews if they would sponsor you or not. With GC you have much better chance to get into programs that you want. The whole process to get into residency however now takes long time, you have to start applying in the fall and go through "Match", get your interviews, and sometime in March see the results of "Match". You may find a hospital that has unmatched slots or needs to fill a spot right away because someone left. In any events, do not accept J-1 or you will be stuck forever.