Witch Bolt cannot prevent spellcasting, it can only interrupt it. From the Basic Rules:
Most spells require a single action to cast, but some spells require a
bonus action, a reaction, or much more time to cast.
Longer Casting Times
Certain spells (including spells cast as rituals) require more time to
cast: minutes or even hours. When you cast a ...
Witch bolt contains no such feature, while Slow does
If witch bolt were to hamper spell casting by the target, it is most likely that this feature would have been added to the spell's description in the same way that slow describes how it hampers spell casting on a target that has failed its save.
If the creature attempts to cast a spell with a casting time ...
You only make a concentration check when you take damage.
The rules for concentration state:
Whenever you take damage while you are concentrating on a spell, you must make a Constitution saving throw to maintain your concentration.
Witch bolt states:
on each of your turns for the duration, you can use your action to deal 1d12 lightning damage to the ...
Use the spell save DC.
The Draconic Presence does not present indeed any indication about the DC for the Wisdom saving throw. Anyway, we can read in the Spellcasting ability section:
Charisma is your spellcasting ability for your sorcerer spells, since the power of your magic relies on your ability to project your will into the world.
and moreover the ...
As the book lacks the information, all we can do is guess what would make most sense, until we eventually get an official errata. Still, there is in my opinion enough reason to think the save would be Will that ruling it that way would not be controversial.
This spell has three tags: Emotion, Enchantment and Mental. All these three tags are associated with ...
I believe it's stated explicitly somewhere but can't seem to find that at the moment. I'll update when I do, but until then we only have it implicitly in the various locations (here, Saving Throws) where modifier calculations are found.
Will saving throws measure how well you can resist attacks to your mind and spirit. They use your Wisdom modifier and ...