Meet with an attorney. This is far too particularized a question for a resolution on a forum such as this one.
Samuel Ouya Maina, Esq. 415.391.6612 firstname.lastname@example.org Law Offices of S. Ouya Maina, PC 332 Pine Street, Suite 707 San Francisco, CA 94104
You can argue first, that you had a contract with an employer, and it has been violated, so you should be entitled to the difference. Now, the question will be: if you do that, will they still keep you employed? Also, employer certified to the US government that this s the wage/ no less than that he is going to pay you... Now, the US government (USCIS) will doubt if the petition was valid... Consult with an attorney!
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The Wage and Hour Division at the US Department of Labor enforces the proper payment of H-1B wages, and underpaid H-1B workers can notify the Agency of possible violations. The following link can be useful for affected H-1B workers: http://www.dol.gov/whd/immigration/h1b.htm
The site contains a H-1B Workers Rights Card that sets forth H-1B workers' rights and procedures for reporting violations.
I agree with Erik CJ Anderson, but keep in mind, as a practical matter, if you file a complaint with the DOL against your employer, or if you sue them for back wages, don't be surprised if you don't completely destroy your relationship with them. You may want to sit down with them in a non-confrontational way and ask them to correct your wage going forward, and to make up your back wages. I certainly wouldn't start with filing a complaint against them. Use that as a last resort.