The idea behind fasting is to get your insulin levels low. Anything with carbohydrates will cause an insulin response by the pancreas and cause insulin levels to rise. Half and half has some milk so will have some milk sugars (lactose) which is a carbohydrate.

So if fasting is your goal it would be best to avoid half and half during your fasting period.

That said it also depends on how much benefit you wish to get from fasting. One tiny container individual portion is going to be a very small amount and very low carbohydrate content. So the insulin response is going to be minimal. If you are diabetic or insulin resistant and wanting to get the most from your fasting to help reverse those conditions, then best to avoid it. If you are metabolically healthy it probably is less significant.

For best health results best to avoid it (for fasting benefit purposes). But the world will not suddenly come to an end if you don't. I used to couldn't hardly drink coffee without cream or something. Never was a natural coffee drinker. But since have gotten used to it black and drink it that way almost every morning now. Having a cup right now with the only "additive" being a couple drops of Lugol's iodine.

If you must have something in my opinion heavy cream would be better than the half and half (again, specifically for fasting benefit purposes only). It would have less of the lactose in it than half and half. Even heavy cream is not absolutely perfect (is not pure fat, still has a few milk solids) but is probably "close enough" as long as you are not using it by the cupful (a little coffee in your cream??? LOL)

I'm not a doctor nor nutritionist, so take what I say for whatever you think my opinion is worth.