I've noticed that some premade digital GM screens I've used say that consequences give you -2, -4 and -6 to your attack value, but can't seem to find this in the core book.
Is this just something I'm misunderstanding, or does it mean that if you, for example, get a mild consequences of "dazed", does your attack value get a -2 on it? As in you attack with Fight +3, but you get a -2 on top of that because of the consequence?
Consequences do not give an ongoing minus to a person's attack value.
The GM screen you're reading is probably alluding to the rules for resolving attacks in a conflict — specifically the part where if someone lands an attack on you, you can "reduce the shift value of the attack" (as the rules put it) by taking a consequence, e.g. your medium consequence (-4) and your first stress box (-1) to absorb an attack worth +5 shifts of harm and avoid getting taken out.
Having that consequence provides no ongoing direct penalty to your actions (or attacks). It's available to be compelled or invoked against you, and the person who gave you the consequence in a conflict gets their free invocation for a one-off +2 bonus or reroll, but there's no inherent ongoing effect other than whatever the consequence aspect says being always true.
No. As you found when you went to the Fate Core book, consequences which you have taken do not give you a minus to your subsequent attacks.
In fact, there is nothing at all in Fate Core which has a mechanical effect like that. Modifiers are always positive. Negative modifiers are avoided and not recommended by the Fate Core designers.
The designers have stated this intention many times in various blog, social media and forum posts, but I think this one captures the spirit very well, while showing how the math is the same when it's mechanically treated as someone else's advantage versus your disadvantage: http://www.evilhat.com/home/consequences-as-positive-currency/
