In　this　paper,　a　modified　Leslie-type　predator-prey　system　with　Holling-type　III　functional　response　is　formulated　to　investigate　the　dynamics　in　the　presence　of　special　Allee　effect　induced　by　fear　factors.　First,　we　calculate　the　first　three　focal　values　by　the　method　of　successor　function　to　ensure　that　the　system　has　an　unstable　weak　focus　of　multiplicity　3.　A　focus-　or　center-type　degenerate　Bogdanov-Takens　singularity　of　codimension　3　and　a　weak　focus　of　multiplicity　1　or　2　together　with　a　cusp　of　codimension　2　are　derived　for　the　system.　Then　multiple　bifurcations　are　explored.　It　is　shown　that　the　system　undergoes　Hopf　bifurcation　of　codimension　3　and　hence　three　limit　cycles　are　generated.　There　exists　another　large　stable　limit　cycle　enclosing　these　three　limit　cycles　by　Poincar　&　eacute;-Bendixson　theorem.　We　demonstrate　that　a　degenerate　focus-type　Bogdanov-Takens　bifurcation　of　codimension　3　can　occur　by　calculating　the　universal　unfolding.　It　is　also　shown　that　a　subcritical,　supercritical　or　degenerate　Hopf　bifurcation　occurs　together　with　a　Bogdanov-Takens　bifurcation.　Finally,　numerical　simulations　are　used　to　support　the　theoretical　results.　The　analysis　results　reveal　that　the　special　Allee　effect　is　beneficial　for　the　persistence　and　diversity　of　ecosystem.