Starting at 2nd level, you can add half your proficiency bonus, rounded down, to any ability check you make that doesn't already include your proficiency bonus.
I could at level 2 add half my proficiency (being 1) to for example Deception making that skill go from 5+1=6.
Now at level 3 I get to add proficiencies and decide that Deception should now be something I am proficient in.
The way I interpret this is that I could keep the 6 and add the 2 from the proficiency because at the time of adding (Jack Of All Trades) I hadn't been proficient in it.
So I'm just asking for clarification.
Best Answer
You cannot gain the bonus from both Jack of all Trades and Proficiency, they are mutually exclusive.
You're misunderstanding the way ability checks work. An ability check is:
The number you have written on your character sheet is not your ability check. It merely represents the combination of your ability modifier and the bonuses and penalties that will generally apply when you make a check of that type.
So when you make a Deception check, you add the relevant ability modifier (Cha), then any bonuses or penalties that apply. If you're proficient in Deception, one of those bonuses is your proficiency bonus. However, the check now includes your proficiency bonus, to Jack of All Trades no longer applies.