How come he's their kid?

Welp... it's major spoilers so read at your own risk.
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So... She and Yehan are both from that independent country... and from different factions. They both loved each other but hid their true identities. She got pregs and gave birth to our cutie in her family, the nie family, without revealing whos the father and without Yehan knowing. Next time he saw her she was badly traumatized and just wanted to get out. So. He erades her memories and implanted Ye Wanwan's (who died) in her giving her a new identity and keeping her by his side.

So mc's identity is fake and she's from strong background? Right?

So do you mean Si Yehan is not from the Si family either?

Welp...
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Basically yes. Not that she knows tho. But it will slowly go that way... she recovering her strength, going to that country etc...

thatss why her brother looked adopted

Si yehan is still a member from the si family because yehan's father is from the si clan and also yehan's mother holds one of the strongest power in the independent state