I'm not entirely sure what the concept of a catchphrase is, but assuming it's essentially a commonly used phrase (e.g. McCoy's "I'm a doctor, not a..." tirade), here's what I've got for my toon, Captain Robin L. Zhang:

General response to a not-so-desirable development in a situation - "Never mind, let's go!"


Upon hearing something he perceives as ludicrous - (Howling laughter followed by an awkward realization) "I'm sorry....urm...that was just in my head...right...?"

On the other hand:

• Chief Tactical Officer Lt. Cmdr. Christine Barber's equivalent of "Cool story, bro." - (Folds arms with a sigh) "That's cool."
  
  
• Security Chief Lt. Cmdr. Mirra Shran, whenever starting a conversation with fellow Andorian and Chief Engineer Lt. Cmdr. Vrin K'vov - (Flirtatious dip of head antenna) "Hey big boy...what'cha doin'?"