Persecute (Verb) = Harass or ill treatment
Synonyms: Abuse, Bully, Hound, Oppress, Trouble, Victimize
Example: You cannot persecute anybody on the basis of his skin colour.
Prosecute (Verb) = Conduct legal proceedings against somebody
Synonyms: Indict, Summon, Sue, Take to Court, Try
Example: The police prosecuted the accused