I’m trying to write a metal song so I would like to know any suggestions for a dark or melodic modulation from e Phrygian to C minor. Preferably on guitar thanks.
Since E Phrygian and C major share the same set of pitches, transitioning to C minor can be fairly straightforward. Transitioning through G major would be the most direct.
However, since you're looking to keep things dark. I suggest moving from an E minor chord to F minor and then to C minor. The F in the F minor chord takes advantage of the characteristic F from the E Phrygian mode, but the F minor chord itself is part of C minor, so makes for a smooth transition.
Another darkish possibility would be to go through B diminished. It is part of both E Phrygian and C Minor, and is also dark as long as that level of dissonance fits in the music.
Similarly, Eb augmented is possible. From E minor, drop the E to Eb and leave the G and B alone. Then move the B up to C to get a C minor chord.
You're composing heavy metal. Especially for extreme metal subgenres like death metal and thrash metal, you don't need smooth modulations with pivot chords. You might need smoother modulations for power metal and maybe some of that symphonic metal stuff, but heavy metal can withstand a jump from E minor chords (in E Phrygian) straight to C minor chords just fine. And, as modulations go, E Phrygian straight to C minor is dark enough.
Take this as an example of how sudden modulations can be in heavy metal (this is admittedly death metal - I think the modulations are clearer in this instrumental version):
Note the Cm-Em chord progression in 1:02-1:05 of this video, with the song modulating straight from a rather chromatic G sharp minor to E minor there.