The
vomiting and twitching might not be something serious. A
cat will naturally twitch when they're in a deep sleep. My cat does it all the time and it's NOT a seizure. If you're seeing only the paws twitching and no other symptoms, then you have nothing to worry about.
The vomiting, depending on how long it's been going on, may not be serious. Sometimes vomiting can be caused from a new diet change and other times it can be caused from hairballs.