This is not a contradiction, because a priori is different data than a posteriori. The point can remain fixed with additional stochastic information; e.g. think about the stochastic model of a mark or of a bolt. In theory, the point is fixed, but in practice, positioning at that point provides uncertainties.
The original a priori data could be kept - i.e. not overwritten -, and, in addition, a posteriori data could be provided as a result. Even for a fixed point, the a posteriori precision might be different.

I didn't try it, but maybe one could artificially introduce "observations of direction 0 gon, vertical zenith angle 0 gon, and distance 0m" and include the stochastic information into that artificial observation as kind of a workaround? For an error ellipsoid, one could introduce artificial observation in the directions of the principal axes.

So, I would like to know is there a way to import fixed points with known variances in JAG3d and adjust the network in a way that these variances affect the results of the adjustment but the imported fixed points remain unchanged?

No, there is no way because this contradict each other. You assume that the points have uncertainties. That means, the positions are only known to a certain extent, i.e., the points are improvable and, thus, not perfectly known (is not fixed).