Nexus of Fate will be exiled.
While there are two replacement effects that wish to affect where
Nexus of Fate is going, the one from
Syncopate is what's known as a self-replacement effect–an effect of the spell itself that modifies the effect that spell would otherwise have. As laid out in CR616.1, if one of the multiple effects trying to modify an event and is a self-replacement effect and the other is not, the self-replacement must be applied first.
Once you apply
Syncopate's replacement to the event
Nexus of Fate's own replacement no longer applies because it's no longer about to be put into a graveyard, so it gets exiled.