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A pathway from one vertex of a quiver to another is a reduced path. We modifythe classical definition of quiver representations and we prove thatsemi-invariant polynomials for filtered quiver representations come fromdiagonal entries if and only if the quiver has at most two pathways between anytwo vertices. Such class of quivers includes finite $ADE$-Dynkin quivers,affine $\widetilde{A}\widetilde{D}\widetilde{E}$-Dynkin quivers, star-shapedand comet-shaped quivers. Next, we explicitly write all semi-invariantgenerators for filtered quiver representations for framed quivers with at mosttwo pathways between any two vertices; this result may be used to studyconstructions analogous to Nakajima's affine quotient and quiver varieties,which are, in special cases, $\mathfrak{M}_0^{F^{\bullet}}(n,1) :=\mu_B^{-1}(0)/\!\!/B$ and $\mathfrak{M}^{F^{\bullet}}(n,1) :=\mu_B^{-1}(0)^s/B$, respectively, where $\mu_B:T^*(\mathfrak{b}\times\mathbb{C}^n)\rightarrow \mathfrak{b}^*\cong \mathfrak{gl}_n^*/\mathfrak{u}$,$B$ is the set of invertible upper triangular $n\times n$ complex matrices,$\mathfrak{b}=\lie(B)$, and $\mathfrak{u}\subseteq \mathfrak{b}$ is the biggestunipotent subalgebra.

Semi-invariants of filtered quiver representations with at most two pathways