I would like to know which sentence is correct:

  1. Shall I bring you an ice cream? or
  2. Shall I bring an ice cream to you?
    Thank you for your support!

Both sentences are fine. The difference is that ‘to you’ in the second sentence suggests that you are bringing/delivering the ice cream to where you live/your address. It would therefore be better to use sentence 1 if you are merely offering to fetch an icecream for someone.

Alan, if we use ‘Shall I bring an icecream for you?’, is there a difference? If so, what?

This suggests that you are being helpful to someone by getting the icecream for someone who possibly can’t for one reason or another get it themselves.

I see. Useful information. Thank you.