More information is needed to determine if you have a qualifying relationship that makes you eligible for permanent resident status. You should consult with an immigration attorney to help you make that determination.
If you're currently in the United States on an H-3 visa, then you are ineligible to file for legal permanent resident status based on your visa status. An H-3 visa is a non-immigrant visa. You need to talk with an immigration attorney to find out if there is someone in your family who is naturalized or with permanent resident status who can apply for family-based permanent residency or see if there's some way an employer-based permanent residence. But your H-3 nonimmigrant visa alone does not have you on a path to permanent residency. You need to talk with an immigration attorney about seeing if you could qualify for employer-based permanent residency if the company you're training under, or some other potential employer, is willing to "sponsor" your application for permanent residency.