Existence of primitive normal pairs over finite fields with prescribed subtrace

Given positive integers $q,n,m$ and aq, where q is an odd prime power and n≥ 5, we investigate the existence of a primitive normal pair (ε,f(ε)) in F_qⁿ over Fq such that STrqⁿ/q(ε)=a, where f(x)=f₁(x)f₂(x)qⁿ(x) is a rational function together with deg(f₁)+deg(f₂)=m and STrqⁿ/q(ε) = ∑0≤ i<j≤ n-1^εqⁱ+qʲ. Finally, we conclude that for $m=3$, n≥ 6 and q=7ᵏ; k, such a pair will exist certainly for all $(q,n)$ except at most $14$ choices.