I slept with the empress and my offspring stands to inherit the throne. How do I benefit?

No, you can't. The child is considered to be legitimate, so you have no official ties to him.

There is an additional complication - you should worry about not getting marriage between close blood relatives. Your legal daughter can marry your unofficial child, forming an alliance with the empire, but their children have a high risk of getting an inbred trait.

When the child is born there is a random chance that one of these two happens:

• the cuckolded partner discovers the child is not theirs in which case you get an event giving you a choice to make the child your dynasty (or not)
• the cuckolded partner accepts the child as their own, in which case there are no further events and the child is considered legally to belong to the official partner for the rest of the game. There are no events in this case that would allow you to somehow reveal that the child is yours.

Since you already have seduction focus and the second case has clearly fired for you, you can continue the seduction game with the empress and hope that at some point the partner discovers she had been cheating on him. At that point, if it's a boy, bring him into your dynasty and plot to kill the children who are ahead of your son.

One can only benefit if the affair was discovered and legitimizes the child. The boon is that you don't have to marry her to gain her titles for your children.

Conditions:

• The impregnated woman must be ruling
• The bastardness must be discovered and you must legitimize the child
• You need to get rid of other valid heirs (in-wedlock boys, other family members with higher gavelkind priority, etc)