In my community, every user should only have one account.
So I need a solution to verify that the specific account is the only one the user owns
I know this is probably nothing you have expected, but...
My suggestion would be to discourage people from creating another account by offering some bonus values if they use the same account for a longer period, a kind of loyalty program. For some reason using a new account gives some advantages. Let's eliminate them. There are a lot of smart people here, so if you share more details on the advantages someone could come up with some idea. I am fully convinced this is on-topic on SO though.