So a while back one of my wife’s uncles found a book which suggested that their family are sayeds, it’s authenticity is unknown.

If it turns out that she is a sayeda, will our children be sayeds even though I’m not a sayed?

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Your children won’t be legally considered Sayeda, since that is transferred paternally. But they will have certain blessings, like being from the progeny of the Prophet and Imams, and being Mahram to them.