Re: "The client's game account has been banned: Banned"
Using steam or origin version is not the reason you got banned, there could be multiply different reasons for a ban.
Please contact the correct department by following the link:
https://help.ea.com/en-in/help/account/Copy%20of%20information-about-banned-or-suspended-accounts/
Read it and follow the steps to send in an ban appeal.
Keep in mind that a ban appeal request may take up to 30 days or more so be patient and wait for the team to investigate and handle the ticket.
Unfortunately we cannot help you in this matter here on ea answers.