Abstract : We construct the triple difference sequence spaces Γ^3 (p∇^3 q)=(Γ^3 )_(p∇^3 q), where p=(θ_uvw^mnk ) is an infinite three-dimensional matrix of Padovan numbers θ_mnk defined by (θ_uvw^mnk )={■(θ_mnk/(θ_(u+5,v+5,w+5)-2),&m≤u,n≤v,k≤w,@0,&m>u,n>v,k>w)┤ and ∇_q^3 is a q-difference operator of third order. We obtain some inclusion relations, topological properties, Schauder basis and α-,β- and γ- duals of the newly defined space. We examine some geometric properties. We introduce and study some basic properties of rough I_λ-statistical convergent of weight g(A),where g:N^3→[0,∞) is a function satisfying g(m,n,k)→∞ and g(m,n,k)↛0 as m,n,k→∞ of triple sequence of Padovan q-difference matrix, where A represent the RH-regular matrix and also prove the Korovkin approximation theorem by using the notion of weighted A-statistical convergence of weight g(A) limits of a triple sequence of Padovan q-difference matrix and also have proved Korovkin approximation theorem by using the notion of weight g(A) limits of a triple sequence space of Padovan q-difference matrix. All the results will certainly motivate the young researchers.