; or (iv) was, on the date of the enactment of this Act— (I) an alien lawfully admitted for permanent residence; or (II) an alien admitted as a refugee under section 207 of the Immigration and Nationality Act ( 8 U.S.C. 1157 ) or granted asylum under section 208 of such Act ( 8 U.S.C. 1158 ). (B) Waiver (i) In general The Secretary may waive the application of subparagraph (A)(i)(III) or any provision of section 212(a) of the Immigration and Nationality Act ( 8 U.S.C. 1182(a) ) that is not listed in clause (ii) on behalf of an alien for humanitarian purposes, to ensure family unity, or if such a waiver is otherwise in the public interest. Any discretionary authority to waive grounds of inadmissibility under such section 212(a) conferred under any other provision of the Immigration and Nationality Act shall apply equally to aliens seeking provisional immigrant status under this section. (ii) Exceptions The discretionary authority under clause (i) may not be used to waive— (I) subparagraph (B), (C), (D)(ii), (E), (G), (H), or (I) of section 212(a)(2) of such Act; (II) section 212(a)(3) of such Act; or (III) subparagraph (A), (C), (D), or (E) of section 212(a)(10) of such Act. (C) Conviction explained For purposes of this paragraph, the term conviction does not include a judgment that has been expunged, set aside, or the equivalent. (D) Rule of construction Nothing in this paragraph may be construed to require the Secretary to commence removal proceedings against an alien. (e) Fees and penalties (1) Standard processing fee Aliens 16 years of age or older who are applying for provisional immigrant status under this subsection, or for an extension of such status, shall pay a processing fee to the Department of Homeland Security in an amount determined by the Secretary. (2) Recovery of costs The processing fee authorized under paragraph (1) shall be set at a level that is sufficient to recover the full costs of processing the application, including any costs incurred— (A) to adjudicate the application