I am not certain I understand your question. If you are saying that you obtained lawful permanent residence through asylum, but that you were not the principal applicant, then you should not have a problem for having traveled to your country. Either way, you should consult an immigration attorney before applying to make certain that you are eligible and will not have any trouble.
As set forth in the minutes of the ASYLUM HQ/NGO LIAISON MEETING on March 6, 2007, USCIS has stated:
"Derivative asylees are permitted to travel to the principal’s country of persecution. Derivative asylees have not been granted asylum on their individual cases so CIS would not seek to terminate their asylum status upon such travel. However, normal procedures would still have CBP questioning the derivative asylees when they re-entered the United States."
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Dean P. Murray
The Murray Law Firm
560 Sylvan Avenue
Englewood Cliffs, NJ 07632
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I agree with my colleagues - if you are the derivative applicant you should not have a problem with DHS if you return to your home country.
Samuel Ouya Maina, Esq. 415.391.6612 email@example.com Law Offices of S. Ouya Maina, PC 332 Pine Street, Suite 707 San Francisco, CA 94104