Can my father who is a lawful permanent resident file an immigrant visa petition on my behalf?

Alex, thank you for your question. With respect to the portion of your question that asks can your father who is a lawful permanent resident apply for an immigrant visa for you, the short answer is yes. You would qualify as a 2B preference and the proper form for this petition is the I-130. Unfortunately there is a substantial waiting period for visa applications for people in your category. The current waiting period is about 9 years.

However, even if your father applies, the petition is approved, and a visa number eventually becomes available for you this may require you to return to your home country to apply for the visa. If you are not in good status in the U.S. at the time your visa becomes available you likely will not qualify for adjustment of status. This might create some additional issues for you. I can't really comment on how it might be an issue for you or what to do because you case is a complicate one because of the pending asylum petition.

In any case, it would probably make since for your father to file a petition for you and get your place in the queue.

Good luck, hope this was helpful.