It should be the house was BUILT IN 1390.
at - signifies a location and 1390 is a year not a place so that would not work
since - means from a particular time to the present so if you use since it means the house is still being built
on - also signifies a location
in - is used to indicate that something is a part of something else either a location, a space or amount of time. So In would be correct