Arcana cleric can be pretty deadly in close quarters due to how Potent Spellcasting interacts with the wizard cantrips you can pick up. Divine Strike only works on your own turn (so not with Warcaster AOs), and Blessed Strikes can only be applied to one target per round. By contrast, Potent Spellcasting procs every single time you deal damage with a cleric cantrip, on turn and off, single target or multiple. Thus, Potent Spellcasting will apply to both the primary and secondary damage of Booming Blade and Green-Flame Blade, including when used for OAs via Warcaster (and yes, you can use GFB with Warcaster, with the caveat that you don't target a second creature). I prefer BB myself, and BB is also a good control spell that can "encourage" an enemy to stay where they are, and because Potent Spellcasting adds to that secondary damage, it strengthens that "encouragement". For an interesting combo, take Crusher and push them 5 feet away so that they're out of melee range and can't retaliate on their turn.

For your second wizard cantrip, I'd actually suggest Create Bonfire. Create Bonfire can actually be used as an AoE (a 5 foot cube is actually a pretty massive fire) by placing it on a corner between four squares, hitting a 2x2 area (technically, by RAW you can hit a 2x3 area by placing it centered on the edge between two squares and rotating the cube 45 degrees, but RAW or not, that's going to be a very hard sell to your DM). Again, Potent Spellcasting will apply to every creature you hit with CB, instead of just one like Blessed Strikes, and it will apply to any hits on subsequent turns after creating the bonfire. Again, this isn't just about straight damage, this also encourages enemies to stay out of the bonfire, making it more effective at blocking off corridors and such. Both BB and CB can be effective control cantrips that also deal a fair amount of damage as a bonus. Clerics also have Word of Radiance, a melee AoE that, again, Potent Spellcasting will boost the damage against each target instead of just one.

Now, clerics don't have a lot of good control spells, though they do have some (Spirit Guardians, for example), so you might want to look at some other caster classes. Wizards have been mentioned a lot, and for good reason. If you're not familiar with Treantmonk's Guide to Wizards then you should definitely check that out, as it focuses a lot more on control. Defense is an issue for wizards, and I see some people suggesting a Hexblade dip or taking Moderately Armored on a race with light armor proficiency; my personal favorite is to dip a level into cleric, though, as that adds a lot of value to a wizard.

If you want a strong meatgrinder wizard, you could look into a Thunderclap Evoker. Potent Cantrip means enemies take half damage even if they pass their save, and Empowered Evocation adds your INT mod to the damage against each target, similar to Potent Spellcasting. This makes it much easier to quickly grind through hordes of weak enemies like goblins. That said, this is a pretty niche trick, so I don't know that it's worth speccing for, especially when there are so many other subclass options for wizards that offer their own interesting combos. But wizards are pretty flexible, regardless of their subclass, so no matter what you pick you'll still have access to tons of great wizard spells.

Sorcadin is another great option. 2 levels of paladin for smites and heavy armor, maybe a dip into Hexblade so you can attack with CHA, and the rest in sorcerer. You get the heavy armor, and access to great control spells on the sorcerer list, and can dump out some heavy damage via smites. You used to be able to twin Booming Blade, consult your DM to see if they might still allow it. Sorcerer also has a neat trick in that you can Quicken a good concentration spell like Web, then use your action to cast a cantrip like Booming Blade, all in the same turn.

Another neat trick is to pick up Flames of Phlegethos and then dip into genielock, specifically efreet. This makes any spell you cast with an attack roll trigger Flame of Phlegethos, punishing anyone who attacks you. You miss out on the damage buff if the spell doesn't natively inflict fire damage, but it gives a lot more flexibility, and allows you to use something like Booming Blade (instead of GFB) for the control it provides while still triggering the fire shield effect. Plus, Fireball is always a good pick; I'm not even super wild about blasting, but Fireball is just that strong, and there's no better control than death.

TL;DR, if you want a melee control caster, then you're probably looking at something built around Booming Blade spam. Cast your concentration spell, then go to town with BB, maybe throwing in the occasional Fireball, Thunderwave, or other non-concentration spell every now and then. Sorcadin is probably your best bet, though Arcana cleric might work as well. For a wizard or druid, you might not want to go for BB, so consider other options (e.g. Wild Shape or Thunderclap spam).

Honorable mention goes to Conquest paladin. Not a full caster, so I'm not sure it counts, but the combination of their aura and several different ways of inflicting fear on enemies make them decent controllers (so long as the enemy isn't immune to fear). Wrathful Smite is cheap and highly effective for locking down a single enemy (note that after the initial save, it uses an ability check on subsequent turns to end the effect early, and because the enemy is frightened, they have disadvantage on ability checks). And of course paladins excel in melee.