alien applying for permanent resident status on a conditional basis under this section, or without the conditional basis as provided in section 21004(c)(2), shall establish that the alien has registered under the Military Selective Service Act ( 50 U.S.C. 3801 et seq. ), if the alien is subject to registration under such Act. (c) Criminal and national security bars (1) Grounds of ineligibility Except as provided in paragraph (2), an alien is ineligible for adjustment of status under this title (whether on a conditional basis or without the conditional basis as provided in section 21004(c)(2)) if any of the following apply: (A) The alien is inadmissible under paragraph (2) or (3) of section 212(a) of the Immigration and Nationality Act ( 8 U.S.C. 1182(a) ). (B) Excluding any offense under State law for which an essential element is the alien’s immigration status, and any minor traffic offense, the alien has been convicted of— (i) any felony offense