at the end of act 1 and 3 Iago discloses reason why he hates the moor? what is it?. Does Iago have evidence to support his suspicion?

His first mention is to Roderigo:

"....I hate the Moor. My cause is hearted. Thine hath no less reason. Let us be conjunctive in our revenge against him. If thou canst cuckold him, thou dost thyself a pleasure, me a sport."

Iago later says:

"I hate the Moor, And it is thought abroad that ’twixt my sheets

He’s done my office. I know not if ’t be true..."

There are rumors that Othello has slept with Iago's wife. As you can see from the above quote, his belief is based upon rumors. He isn't sure the suspicion is reality.