While the U.S. Constitution doesn't explicitly state "no taxation without representation," the principle is reflected in the Origination Clause (Article I, Section 7) that requires all revenue bills to start in the House of Representatives (the people's directly elected body) to ensure consent for taxation.
I think the sort of case you envision would need to be a challenge to "partisan" gerrymandering (i.e., lack of representation as a Democrat in your state because the map is so gerrymandered that republicans are overrepresented to an extent so extreme that your right to representation has been violated.
Tragically for the nation, in Rucho v. Common Cause (2019), Roberts, Thomas, Alito, Gorsuch, and Kavanaugh declared challenges to a partisan gerrymandered map are "non-justiciable" at the federal level. In other words, the Federal courts can't weigh in on claims of partisan gerrymandering.
The sane voices of dissent to the horrible decision, Kagan, Ginsburg, Breyer, and Sotomayor, argued that the majority abandoned the Court's duty to protect democracy, asserting that federal courts could and should address partisan gerrymandering because it undermines fair elections and equal participation, with some lower courts already developing workable standards to evaluate these harmful practices. They contended the majority's refusal to act would encourage more extreme polarization and that modern technology makes gerrymandering more precise and damaging than ever. (As we are seeing.)
Rucho v. Common Cause is another of the horrific decisions that must be reversed if we are to have a hope in hell of quickly ushering in change for the better.
You might be able to bring a case of some sort in state court. That would depend on the sort of protections in your state constitution that could be invoked. Voters have brought challenges to partisan gerrymandering in state courts with mixed success. (e.g., successful claims in Wisconsin, Pennsylvania, and North Carolina while New Hampshire found claims of partisan gerrymandering non-justiciable under its state law.)