5e doesn’t really have a fun counter mage. You can play a wizard with counterspell and silvery barbs sure, but then you’re a wizard who shuts down other wizards. I’m looking for the mundane characters who wrestle control of spells in effect or prevent their casting to begin with. Not out of some desire to win a wizarding duel, but because they know that letting a wizard cast spells could mean the end of their mission.
I couldn’t decide if a subclass or new class was the way to go, so you may end up seeing a new class come in a couple weeks, if this doesn’t exactly sit well with me.

Spellthief
A rogue archetype for 5e
Disenchant: Starting at 3rd level, you can shut down ongoing magical effects with a well-placed strike. If you would deal sneak attack damage against a creature concentrating on a spell or effect, you can forgo your sneak attack damage. If you do, instead, the creature automatically fails their saving throw to concentrate.
Bonus Proficiencies: When you choose this archetype at 3rd level, you gain proficiency with the arcana skill, and wisdom saving throws.
Wrest Control: Starting at 9th level, when you disenchant a spell or effect, you can choose to wrest control. You can begin concentrating on the spell or effect, instead of your target. Additionally, you can choose new targets for the spell or effect immediately using your ability scores in place of the original casters. You can still only concentrate on one thing at a time.
Disjunction: At 13th level, you gain the ability to alter the properties of magical items. If you would deal sneak attack damage against a creature concentrating on a spell or effect, you can forgo your sneak attack damage. If you do, any items the creature has attuned are unattuned, and any charged items have their remaining charges set to 0. In addition, any charged items in your possession regain a charge (Note you can only forgo your sneak attack damage once. After you’ve done so, its gone, and you can’t use both abilities).
Sever the Weave: Starting at 17th level, you can rob a creature of their spellcasting abilities for longer and longer. If you successfully disenchant a creature, that creature cannot use that same spell or ability until the end of a long rest.