You can use either James’s house or James’ house. Both are acceptable depending on what style guide you follow.
“James’s house” is correct if you are following the Chicago Manuel of Style and “James’ house” is correct if you are following the Associated Press Stylebook.
James’s/James’ House Examples
I went over to James’s house last night.
James’s house is over there.
James’s house has a swimming pool.
St James’s hospital is in Dublin.
St James’s church is in Newcastle.
St James’s Way is the English name for El Camino de Santiago.
Choosing “James’s” or “James’” is up to you, just make sure to be consistent and stick to the same one every time.
Is it James family or James’s family?
Remember that you need an apostrophe to show possession. James’s family or James’ family are correct depending on the style guide that you follow.
If you are talking about more than one James(plural of James), you can use “Jameses”.