In　this　paper,　we　propose　a　discrete　amensalism　model　incorporating　cover　and　saturation　effect.　The　discrete　model　is　derived　from　its　continuous　counterpart　using　the　piecewise　constant　parameter　method.　First,　we　determine　the　equilibria,　outline　the　conditions　for　their　existence,　and　analyze　their　local　stability　properties.　Subsequently,　by　employing　discrete　equation　deflation　and　iteration　methods,　we　establish　a　set　of　sufficient　conditions　that　ensure　the　global　attractivity　of　the　system.　Our　analysis　demonstrates　that　the　size　of　the　cover　and　the　natural　growth　rate　of　the　second　population　significantly　influence　the　global　attractivity　of　the　system.　Next,　we　investigate　the　existence　of　both　flip　bifurcation　and　transcritical　bifurcation　near　the　positive　and　boundary　equilibria　under　certain　conditions,　utilizing　the　central　manifold　theorem　and　bifurcation　theory.　To　control　chaos　arising　from　flip　bifurcation,　we　implement　feedback　control　strategies,　specifically　the　hybrid　control　method.　Finally,　numerical　simulations　verify　the　feasibility　of　our　theoretical　results.　Our　research　reveals　that　both　the　presence　of　cover　and　saturation　effect　enhance　the　density　of　the　first　population,　while　an　increase　in　the　amensalism　coefficient　c1　ultimately　leads　to　the　extinction　of　the　first　population.