My fiance's ex just got married to a registered sex offender. My fiancé and his ex have a daughter together. Legally, can the registered sex offender live with the daughter?

It depends on the level of his offense. What was he convicted of? Peeing in public? Child molestation? Rape?

It depends on the level of his offense. What was he convicted of? Peeing in public? Child molestation? Rape?
I was just looking online And found it and was quite shocked. I haven't been able to even tell my fiancé yet because he is at work. But all it said online was indecent liberties with a minor the age of 14

Again the circumstances here might shock you less. For example was he a 16 yr old feeling up his girlfriend? Or what? As a registered sex offender, he likely has a Probation Officer. This PO would likely have to approve the marriage and I doubt if it would have been approved if he presented a danger to the child.

But I don't know the whole story (neither do you btw). If you fiancée feels that your daughter is now at risk, then he should go to court and petition for a modification in the custody order. Essentially to become primary custodian and limit the mother to supervised visits.

Whether the court will agree depends on the exact circumstances regarding the step dad's sex offense.

This IS a cause for concern and the first thing your fiancée should do is talk to his daughter about inappropriate touching. He should NOT however, specifically warn her about her new step dad, just in general. But before going off and panicking, you need to know the full facts.