pgAdmin IV and PostgreSQL 12.0: ERROR: schema "public" already exists
Well, I was able to solve my problem by another path.

I suspected the problem was related to pgAdmin III and not PostgreSQL, then I opened my remote server through pgAdmin IV and I backed my remote database up. 

After that, on pgAdmin IV, I restored the database and it worked fine, with no error.

Then, I believe the problem is related to creating a backup on pgAdmin III and restore it on pgAdmin IV. 

If someone gets the same error in the future, please, use just pgAdmin IV to avoid problems.