Since - as I discussed in another thread - I want my future D&D campaigns to feature NPC fighters that can counterspell, it seems only right to offer such abilities to interested players as well. After all, I personally played the Wizard Slayer kit in Baldur's Gate II ( which used the 2nd edition system), and was pleased with the results.

The design goal was to make a fighter who was as effective at disrupting magic shenaningans as a full caster and felt like he could easily serve as a bodyguard or battlefield specialist in the campaign world. To that end I gave him straightforward access to Counterspell, Dispel Magic, and a few more utility effects. In exchange he loses the raw damage potential of something like the Champion archetype. I fully acknowledge that this isn't an archetype that will appeal to everybody and doesn't need to be.

I decided not to give him Magic Resistance or full-blown immunity because that would be too much. I don't want him to be able to shut down casters completely. If he really wants to put even more pressure on then he can just take the Mage Slayer feat from the 5e PHB.

There may be some objection to the ability to cast Detect Magic at will, but the 5e Warlock can gain that ability at 2nd level in addition to another spell slot and Warlock ability, so I don't give a fuck.

FIGHTER – SPELLBREAKER ARCHETYPE
In a world where magic users can subvert your mind, imprison you body, and escape danger with a few words and gestures there is a serious demand for effective countermeasures. Spellbreakers are elite soldiers who meet this need by learning just enough of the arcane arts to consistently foil them. Many kings owe their lives to the timely intervention of a spellbreaker bodyguard, and many would-be conqueror wizards have watched their fiendish magical tactics evaporate from the battlefield shortly before a well placed sword stroke took their lives.

Spellbreakers do not consider themselves true casters, just specialists in a very particular form of defense. They do not necessarily hate magic or magic users, but they are always calculating the best way to take down any such individual they meet, just in case.

Casting Spellbreaker Spells
Some of your class features allow you to cast spells. See chapter 10 for the generals rules of spellcasting. Intelligence is your spellcasting ability.

Identify Magical Threats
The first step to ending a magical threat is to realize that magic is at work in the first place. Starting at 3rd level, you can cast Detect Magic at will, without expending a spell slot.  
In addition, you gain proficiecy in the Arcana skill. If you are already proficient in it, you gain proficiency in either Insight, Investigation, or Religion instead.

Spellbreaking
Starting at 3rd level, you can either cast Counterspell or Dispel Magic once per long rest.

Scryjamming
Starting at 7th level, you can cast Nondetection once per long rest. You must still pay for its material component.

Improved Spellbreaking
Starting at 10th level, you regain your ability to cast Counterspell or Dispel Magic after both short and long rests.
In addition, when you cast Counterspell or Dispel Magic, you add your proficiency bonus to the ability checks required by those spells.

Superior Spellbreaking
Starting at 15th level, instead of casting Counterspell or Dispel Magic with your Spellbreaking feature, you may choose to cast Globe of Invulnerability.
In addition, when you cast Counterspell or Dispel Magic, you are considered to have cast it with a 4th level spell slot.

Improved Scryjamming
Starting at 18th level, you may cast Mind Blank instead of Nondetection when using your Scryjamming feature.

I'm not expert enough with the rules to know if these abilities are balanced, but I love the basic approach.

After thinking about it for a day, I've altered the design a little. Main change is I've made it so the Counterspell/Dispel recharges after short and long rests at level 3, and I've moved the spell slot adjustment down to level 10. I also renamed Superior Spellbreaking.

FIGHTER – SPELLBREAKER ARCHETYPE
In a world where magic users can subvert your mind, imprison you body, and escape danger with a few words and gestures there is a serious demand for effective countermeasures. Spellbreakers are elite soldiers who meet this need by learning just enough of the arcane arts to consistently foil them. Many kings owe their lives to the timely intervention of a spellbreaker bodyguard, and many would-be conqueror wizards have watched their fiendish magical tactics evaporate from the battlefield shortly before a well placed sword stroke took their lives.

Spellbreakers do not consider themselves true casters, just specialists in a very particular form of defense. They do not necessarily hate magic or magic users, but they are always calculating the best way to take down any such individual they meet, just in case.

Casting Spellbreaker Spells
Some of your class features allow you to cast spells. See chapter 10 for the generals rules of spellcasting. Intelligence is your spellcasting ability.

Identify Magical Threats
The first step to ending a magical threat is to realize that magic is at work in the first place. Starting at 3rd level, you can cast Detect Magic at will, without expending a spell slot.  
In addition, you gain proficiecy in the Arcana skill. If you are already proficient in it, you gain proficiency in either Insight, Investigation, or Religion instead.

Spellbreaking
Starting at 3rd level, you can either cast Counterspell or Dispel Magic once per short or long rest.

Scryjamming
Starting at 7th level, you can cast Nondetection once per long rest. You must still pay for its material component.

Improved Spellbreaking
Starting at 10th level, when you cast Counterspell or Dispel Magic, you add your proficiency bonus to the ability checks required by those spells.
In addition, when you cast Counterspell or Dispel Magic, you are considered to have cast it with a 4th level spell slot.

Invulnerable Spellbreaking
Starting at 15th level, instead of casting Counterspell or Dispel Magic with your Spellbreaking feature, you may choose to cast Globe of Invulnerability.

Improved Scryjamming
Starting at 18th level, you may cast Mind Blank instead of Nondetection when using your Scryjamming feature.