For the trefoil, one way to construct the knot is to take the 2-variable *complex* parameterisation:
a^2 = b^3, |a|^2 + |b|^2 = 1
I think you want |a|^2 = |b|^2 = 1/2 (a torus) rather than |a|^2 + |b|^2 = 1 (a 3-sphere). It makes sense that to define a 1-dimensional curve in C^2, which is R^4 with some extra structure, we need 3 real equations, not 2.
The first of these equations is a complex constraint (therefore two real constraints). Taking absolute values of the first equation gives: |a|^2 = |b|^3 which, together with the second equation, results in: |b|^3 + |b|^2 = 1 which implies that |b| is the unique positive real root of that cubic equation (and therefore |b| ~= 0.754878). This, in turn, forces |a| to be a constant, so (a, b) lies on a Clifford torus as you require. Best wishes, Adam P. Goucher