This　paper　proposes　a　discrete　amensalism　with　the　BeddingtonDeAngelis　functional　response　response　and　fear　effect　on　the　first　species.　By　comparison　and　study　of　different　bifurcations,　the　introduction　of　the　Beddington-DeAngelis　functional　response　not　only　increased　the　dynamical　behaviour　of　the　system,　including　the　emergence　of　pitchfork　bifurcation　and　fold　bifurcation,　but　also　reduced　the　rate　of　extinction　of　the　first　species.　Furthermore,　we　analyze　the　influence　of　the　fear　effect　on　the　system,　specifically　focusing　on　the　boundary　equilibrium　E2　and　the　positive　equilibrium　E1　&　lowast;.　Our　findings　reveal　that　when　the　second　species　is　in　a　chaotic　state,　due　to　the　persistence　of　the　second　species,　the　fear　effect　may　have　increased　the　stability　of　the　first　species　or　accelerated　the　extinction　of　the　first　species;　when　the　second　species　is　stable,　the　fear　effect　plays　an　essential　part　in　maintaining　the　stability　of　the　first　species.　Moreover,　an　appropriate　fear　effect　promotes　the　coexistence　of　the　first　and　second　species.　However,　if　the　fear　effect　becomes　excessively　large,　it　directly　results　in　the　extinction　of　the　first　species.　The　discovery　further　enhances　the　understanding　of　the　influence　generated　by　amensalism　through　the　fear　effect.