"The first sentence of INA 214(b) states that: "every alien (other than a nonimmigrant described in subparagraph (l) or (v) of section 101(a)(15), and other than a nonimmigrant described in any provision of section 101(a)(15)(H)(i) except subclause (b1) of such section) shall be presumed to be an immigrant until he establishes to the satisfaction of the consular officer, at the time of application for a visa, and the immigration officers, at the time of application for admission, that he is entitled to a nonimmigrant status under section 101(a)(15)." It means that, with limited exceptions, all visa applicants are presumed to be immigrants (and hence not eligible for non-immigrant visas) unless and until they satisfy the consular officer that they qualify for one of the nonimmigrant visa categories. Per section 291 of the INA, the burden of proof is on the applicant. If a non-immigrant visa applicant does not meet this burden of proof to the satisfaction of the consular officer, then by law the alien is considered to be an applicant for immigrant status and should not receive a nonimmigrant visa." You were denied a B1/B2 visitor's visa because, by filing an asylum application for you, your parents demonstrated that you intend to stay in the U.S. It does not matter if you did not sign that application: a consular officer would be justified in believing that the application would not be filed without your knowledge and consent. So now, you will face this problem every time you try to enter the U.S. - you would have to try proving that your circumstances changed and that you will not try to stay in the U.S. beyond the term of your non-immigrant admission. Proving a negative, especially a future negative, is almost impossible; but, if you show to the consul that, for example, you got married, have children, and neither your spouse nor children will be accompanying you to the U.S., or that you found a high-paying job, or started a profitable business, or have large contracts in your own country, you might succeed. As to your present predicament, it is quite special. You see, the requirement to prove that you do not intend to become an immigrant in the U.S. does not apply to H1B visas. So, under the law, you (and your spouse, if you have one) can apply for H1B - and receive it if the application will be done right. This does not mean that USCIS will not deny the application; so you have to be prepared to appeal the denial - and for the resulting delay. To sum it all up: Yes, you can apply for H1B. Just make sure you have a good immigration attorney....
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