I have a Square taper BB.
 

I have a square taper BB and I am thinking of changing the crankset so as to have a shorter crank arm. Can I or should I change the square to a modern external bearing BB or is that not possible? I am currently using the stock FSA crank and want to go to a Shimano 105 or Sora 50/34 but I am concerned that the chain line will be wrong due to the external bearing. The bike is a 2019 Quick 3.
Thank you in advance, Frank.

Yes, the external bearing matches the chainline of the square taper spindle. Match the crank to the number of cassette cogs. Claris for 8-speeed, Sora for 9, Tiagra for 10.

most bikes can take whatever crankset and compatible BB that goes with the crankset. match the width of the frame's BB shell and the appropriate type of crankset for your bike.

And its threading.

Thank you all. I have done some more research and as my Quick is a 9 speed I will go with a Sora. Thanks again all.
Frank.

If it is a BSA threaded 1.37 inch x 24 tpi then it's very likely you can put a more modern BB and crankset on it. Width of your BB shell will become your major concern.

Chain line becomes much less a concern when you get away from square tapers. You just need to make sure the crankset is made for bikes with the rear spacing that yours is. Sometimes that's hard to glean from the specs, but fair to say that if you consider what type bike all the other components of that cranksets group is made for, then you can be fairly reassured by that the chain line will be correct. Also consider if that group is meant for bikes that have a particular rear axle spacing as that will affect the chain line the crank is designed for. 130 mm? 135 mm? Something else?

I like my Shimano Hollowtech II cranks that I put in BSA threaded bikes from the 70's and 90's. I can't find any reason to have a desire to return to square tapers.

Sounds like a BSA BB. I didn't bother to mention alternatives because I've found those to be rare. If OP is in Europe or looking at vintage bikes, that might be a different story. In my six years working in bike shops, I encountered an Italian BB once. Just not common where I live, I suppose.

With it being a quick it wouldn't be anything other then a BSA bb. You need to work on more italian bikes, I've had a few of them and worked on plenty over the years. Also have an old tandem running french thread external cup thanks to Phil Wood.