Inspired by this question. Can current be induced in a superconductor?
Magnetic flux of a magnet cannot enter a perfect conductor. Again moving electrons, protons produce magnetic field (and thus magnetic flux). So what about the magnetic flux of the charged particles inside the perfect conductor (those protons and electrons which make the perfect conductor)? can magnetic field exist inside the conductor and just cannot enter from outside? If the question is not clear please inform me.
Edit: I realized I misunderstood the question - I'm used to dealing with superconducting coils, so my answer referred to the flux through the middle of a coil of superconductor.
No - whatever flux existed through the middle of a coil of superconductor when it became a superconductor (usually, when it was cooled below its $T_c$) is locked into the coil. Any additional magnetic flux changes around the superconductor are expelled by inducted EMFs.
In superconducting magnets, usually the superconducting coils are charged by induction while they are above $T_c$ (and therefore not yet superconducting), then they are cooled down; as long as they stay cool and in the superconducting state, the flux through the coil will not change, and the coil acts like a permanent magnet.
Also, it sounds like you think protons are moving around in superconductors, which is not the case - just the electrons.
This is a question of scale. (And an absolutely perfect conductor is something that does not exist).
Superconductors have a band gap that allows dissipation free currents for certain frequencies/wave vectors and only up to certain external fields. If you are beyond that range (e.g. when just turning a field on instantaneously) Cooper pairs will be broken by the interaction with a field and the this will allow a loss mechanism.
The model of superconductivity is an effective field theory (again valid for long wavelengths/low frequencies). In this theory fields on the scale of the fields around single electrons/ions in the lattice are averaged out.
The same holds for an ideal metallic conductor (as $T \to 0$ a defect free metal would also conduct dissipation free for currents with $\omega \to 0$ and $k \to \infty$; but it would not show the Meißner-Ochsenfeld effect), but the effective mass of the electrons would imply a finite ac conductivity.
The real world is "granular", and the description of the smooth macroscopic electromagnetic field (where the internal fields are hidden in the electric polarization resp. magnetization and for which you predict the properties in the effective theories at long scales) will just break down at some scale.
The basic equation relating the fields in vacumn H and those in matter B is the relation $B=H+4\pi M$ where M is the magnetic moment per unit volume called magnetization. Outside matter $M=0$ and therefore $B=H$. For perfect conductor there are two field inside that cancel each other. Inside $M=-H/4\pi$ hence $B=H+4\pi(-H/4\pi)=0$. M arises due to motion of charges inside the superconductor. Now when we talk about the fields inside the conductor they really are the average taken over a space containing many charged particles. So the B, H and M are in fact averages taken over a small volume but small enough to contain a large number of charged particles.
