It's difficult to give a definitive answer because of the ambiguity of words like "heretic" and "persecute". I presume that if Mr X says to Mr Y, "No, I disagree with you", that's not persecution. If he has him tortured and killed over the disagreement, that pretty clearly is persecution. But there's a wide range in the middle. If X tells people that Y is a dangerous kook and they shouldn't associate with him, is that persecution? What if so many people follow X that Y is completely ostracized from society, can't get a job, etc?
All that said, I suspect the first case would be the repudiation of Arianism at the Council of Nicaea in AD 325. The Arians were exiled and their books banned, which I think qualifies as persecution. This took place shortly after Emperor Constantine converted to Christianity, and so suddenly Christians went from being outlawed and persecuted themselves to having political power and influence.
Constantine was an emperor, i.e. a dictator, so it's not surprising that when he learned that his new-found religion was facing division and disagreement, he decided to step in and "solve" the problem by declaring which side was right and ordering everyone to fall in line or else. AFter all, that's what he would do if his generals disagreed about how to wage a war, or if his bureaucrats disagreed about how to administer some law.