How can I find my boyfriend accounts for website on my phone for free

You ask him. Is there a reason you have to be a nosey girlfriend? Has he given you a reason not to trust him?

You can not, even paid sites can not do this. He can use any number of email addresses, user names. It is not possible.

Asking this question shows you do not want to be his girlfriend; You want to be his owner. Unless he wants to be owned, which is very complicated, you may wish to reconsider your relationship.

What's wrong with NOT knowing what websites he has accounts for?

If you don't trust him and feel you need to check up on him then it is better to end the relationship and move on.