You can definitely petition for and wait adjudication of a U visa while in the USA legally or not. You do not need to leave to seek U visa from abroad.
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Your question is a bit confusing as you indicate you will be applying for the H1 B and at the same time want to apply for a U visa. Remember the U visa is not available for just any crime but for only certain enumerated crimes- which an immigration attorney can assist you with. If you are applying for H1 B not clear why you would need to apply under the U . Consult an immigration attorney who knows both types of cases to see if the U visa is even possible.
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Since any decision you must make deals with your immediate future in the U.S. it compels me to suggest that you need to have a full and legally correct understanding of your options stated during a personal meeting with a practicing immigration attorney.
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