Or did they believed it was him through out dark shadows entire run despite some of the people who believes his innocence?

he was never cleared, but it was never brought up again either

He was sent to windcliff and released at the start of the adam and eve storyline

I don't think he was ever officially cleared. No new evidence came up to suggest he was innocent. If memory serves me right, he was institutionalized because he was deemed criminally insane--in other words, he was considered not guilty by reason of insanity. Julia managed to get him released by saying he had been rehabilitated enough to rejoin society.