(しょうこ) Physical evidence, such as a footprint, or,  “This green tap-water is evidence of pollution.” Also, this is the word one uses about evidence at trials, not 証.
(しょうめい) Proof, mathematical or logical.
(あかし) Somewhere in between 証明 and 証拠. You’d typically use 証 when you’re talking about evidence of God, such as miracles. Or you’d challenge someone:“You say you’re honest and give to charity, but do you have any evidence of this?” Unlike 証拠、 証 does not have to be physical, it can be verbal.   NP
(しょうげん) Verbal testimony given in court