  In this paper, we consider the tensor product of local Weyl modules for
$\mathfrak{sl}_{n+1}[t]$ whose highest weights are multiples of the first and
$n^{th}$ fundamental weights. We determine the graded character of these tensor
product modules in terms of the graded character of local Weyl modules and
prove that these modules admit a filtration whose successive quotients are
either truncated Weyl modules or fusion products of Demazure modules.
Furthermore, we establish that the truncated Weyl modules appearing as
quotients in the filtration of tensor products of local Weyl modules of
$\mathfrak{sl}_3[t]$ are indeed isomorphic to fusion products of irreducible
$\mathfrak{sl}_3[t]$-modules which establish the independence of a family of
fusion product modules of $\mathfrak{sl}_3[t]$ from the set of its evaluation
parameters.
