The use of “then” here is an adjective, and sounds better before the verb. They’re both pretty much the same As far as meaning goes, but your second example says “them,” which is of course an entirely different word (and would change the meaning). Is that what you meant or is it a typo?

Also, other ways you can say this:

• “The king reigning during that time”
• “The king reigning at that time”

The use of “then” here is an adjective, and sounds better before the verb. They’re both pretty much the same as far as meaning goes.

Also, other ways you can say this:

• “The king reigning during that time”
• “The king reigning at that time”