Unlink Square Enix ID from PSN account
Solution 1:
Have You tried to enter account at Square Enix webpage under Your ID and ask for password recovery with a suggestion of a new e-mail? Another thought is to create a new account with this ID if for some reason they have connected You to a non-existing one or to simply create a new account and bind it with your PSN.
If You’re from those players who create new acc on PSN to get free PS+ for two weeks and/or do not care about Your trophies – simply delete this account and make a new one.
Don't forget to delete all data about credit cards and other payment IDs until You solve this problem.